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  • 101.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries2008Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 213, nr 1, 56-70 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A method where polygon corners in Schwarz-Christoffel mappings are rounded, is used to construct mappings from the upper half-plane to regions bounded by arbitrary piecewise smooth curves. From a given curve, a polygon is constructed by taking tangents to the curve in a number of carefully chosen so called tangent points. The Schwarz-Christoffel mapping for that polygon is then constructed and modified to round the corners.Since such a modification causes effects on the polygon outside the rounded corners, the parameters in the mapping have to be re-determined. This is done by comparing side-lengths in tangent polygons to the given curve and the curve produced by the modified Schwarz-Christoffel mapping. The set of equations that this comparison gives, can normally be solved using a quasi--Newton method.The resulting function maps the upper half--plane on a region bounded by a curve that apart from possible vertices is smooth, i.e., one time continuously differentiable, that passes through the tangent points on the given curve, has the same direction as the given curve in these points and changes direction monotonically between them. Furthermore, where the original curve has a vertex, the constructed curve has a vertex with the same inner angle.The method is especially useful for unbounded regions with smooth boundary curves that pass infinity as straight lines, such as channels with parallel walls at the ends. These properties are kept in the region produced by the constructed mapping.

  • 102.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Modified Schwarz-Christoffel mappings using approximate curve factors2009Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 233, nr 4, 1117-1127 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Schwarz–Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz–Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.

    In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C1 regularity, C regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.

    Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz–Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C) boundary curve can be achieved.

  • 103.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Modified Schwarz–Christoffel mappings using approximate curve factors2009Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 233, nr 4, 1117-1127 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The Schwarz–Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz–Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.

    In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C1 regularity, C regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.

    Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz–Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C) boundary curve can be achieved.

  • 104.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Numerical Conformal mappings for regions Bounded by Smooth Curves2006Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    Inom många tillämpningar används konforma avbildningar för att transformera tvådimensionella områden till områden med enklare utseende. Ett exempel på ett sådant område är en kanal av varierande tjocklek begränsad av en kontinuerligt deriverbar kurva. I de tillämpningar som har motiverat detta arbete, är det viktigt att dessa egenskaper bevaras i det område en approximativ konform avbildning producerar, men det är också viktigt att begränsningskurvans riktning kan kontrolleras, särkilt i kanalens båda ändar.

    Denna avhandling behandlar tre olika metoder för att numeriskt konstruera konforma avbildningar mellan ett enkelt standardområde, företrädesvis det övre halvplanet eller enhetscirkeln, och ett område begränsat av en kontinuerligt deriverbar kurva, där begränsningskurvans riktning kan kontrolleras, exakt eller approximativt.

    Den första metoden är en utveckling av en idé, först beskriven av Peter Henrici, där en modifierad Schwarz-Christoffel-avbildning avbildar det övre halvplanet konformt på en polygon med rundade hörn.

    Med utgångspunkt i denna idé skapas en algoritm för att konstruera avbildningar på godtyckliga områden med släta randkurvor.

    Den andra metoden bygger också den på Schwarz-Christoffel-avbildningen, och utnyttjar det faktum att om enhetscirkeln eller halvplanet avbildas på en polygon kommer ett område Q i det inre av dessa, som till exempel en cirkel med centrum i origo och radie mindre än 1, eller ett område i övre halvplanet begränsat av två strålar, att avbildas på ett område R i det inre av polygonen begränsat av en slät kurva. Vi utvecklar en metod för att hitta ett polygonalt område P, utanför det Omega som man önskar att skapa en avbildning för, sådant att den Schwarz-Christoffel-avbildning som avbildar enhetscirkeln eller halvplanet på P, avbildar Q på Omega.

    I båda dessa fall används tangentpolygoner för att numeriskt bestämma den önskade avbildningen.

    Slutligen beskrivs en metod där en av Don Marshalls så kallade zipper-algoritmer används för att skapa en avbildning mellan det övre

    halvplanet och en godtycklig kanal, begränsad av släta kurvor, som i båda ändar går mot oändligheten som räta parallella linjer.

  • 105.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical Conformal Mappings for Regions Bounded by Smooth Curves2006Licentiatavhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    In many applications, conformal mappings are used to transform twodimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.

    This thesis treats three different methods for numerically constructing conformal mappings between the upper half–plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.

    The first method is built on an idea by Peter Henrici, where a modified Schwarz–Christoffel mapping maps the upper half–plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.

    The second method uses the fact that a Schwarz–Christoffel mapping from the upper half–plane or unit circle to a polygon maps a region Q inside the half–plane or circle, for example a circle with radius less than 1 or a sector in the half–plane, on a region Ω inside the polygon bounded by a smooth curve. Given such a region Ω, we develop methods to find a suitable outer polygon and corresponding Schwarz–Christoffel mapping that gives a mapping from Q to Ω.

    Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.

    Finally, we use one of Don Marshall’s zipper algorithms to construct conformal mappings from the upper half–plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

  • 106.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical Conformal Mappings for Waveguides2010Inngår i: Computational Mathematics: Theory, Methods and Applications, Hauppauge NY, USA: Nova Science Publishers , 2010Kapittel i bok, del av antologi (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with  varying direction and cross-section can, if the variations takes  place in only one dimension at a time be re-formulated as a  two-dimensional scattering problem. By using the so-called  Building Block Method, it is possible to construct the  scattering properties of a combination of scatterers when the  properties of each scatterer are known. Hence, variations in the  waveguide geometry or in the boundary conditions can be treated   one at a time.  We consider in this work acoustic scattering, but the same  techniques can be used for both electro-magnetic and some quantum  scattering problems.  By suppressing the time dependence and by using the Building Block  Method, the problem takes the form of the Helmholtz equation in a  waveguide of infinite length and with smoothly varying geometry and  boundary conditions.  A conformal mapping is used to transform the  problem into a corresponding problem in a straight horizontal  channel, and by expanding the field in Fourier trigonometric series,  the problem can be reformulated as an infinite-dimensional ordinary  differential equation. From this, numerically solvable differential  equations for the reflection and transmission operators are  derived.  To be applicable in the Building Block Method, the numerical  conformal mapping must be constructed such that the direction of the  boundary curve can be controlled. At the channel ends, it is an  indispensable requirement, that the two boundary curves are (at least)  asymptotically parallel and straight. Furthermore, to achieve  bounded operators in the differential equations, the boundary curves  must satisfy different regularity conditions, depending on the  properties of the boundary.  Several methods to accomplish such conformal mappings are  presented. The Schwarz-Christoffel mapping, which is a natural starting point and for which  also efficient numerical software exists, can be modified in  different ways to round the polygon corners, and we show algorithms  by which the parameter problem can be solved after such  modifications. It is also possible to use the unmodified Schwarz-Christoffel mapping for  regions with smooth boundary, by constructing an appropriate outer  polygon to the considered region.  Finally, we show how a so-called  zipper algorithm can be used for waveguides.

  • 107.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Numerical Conformal Mappings for Waveguides2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with varying direction and cross-section can be re-formulated as a two-dimensional scattering problem, provided that the variations take place in only one dimension at a time. By using the so-called Building Block Method, it is possible to construct the scattering properties of a combination of scatterers when the properties of each scatterer are known. Hence, variations in the waveguide geometry or in the boundary conditions can be treated one at a time. Using the Building Block Method, the problem takes the form of the Helmholtz equation for stationary waves in a waveguide of infinite length and with smoothly varying geometry and boundary conditions. A conformal mapping is used to transform the problem into a corresponding problem in a straight horizontal waveguide, and by expanding the field in Fourier trigonometric series, the problem can be reformulated as an infinite-dimensional ordinary differential equation. From this, numerically solvable differential equations for the reflection and transmission operators are derived. To be applicable in the Building Block Method, the numerical conformal mapping must be constructed such that the direction of the boundary curve can be controlled. At the channel ends ,it is an indispensable requirement, that the two boundary curves are (at least) asymptotically parallel and straight. Furthermore, to achieve bounded operators in the differential equations, the boundary curves must satisfy different regularity conditions, depending on the boundary conditions. In this work, several methods to accomplish such conformal mappings are presented. The Schwarz–Christoffel mapping, which is a natural starting point and for which also efficient numerical software exists, can be modified in different ways in order to achieve polygons with rounded corners. We present algorithms by which the parameters in the mappings can be determined after such modifications. We show also how the unmodified Schwarz–Christoffel mapping can be used for regions with a smooth boundary. This is done by constructing an appropriate outer polygon to the considered region.Finally, we introduce one method that is not Schwarz–Christoffel-related, by showing how one of the so-called zipper algorithms can be used for waveguides. Keywords: waveguides, building block method, numerical conformalmappings, Schwarz–Christoffel mapping, rounded corners method, approximate curve factors, outer polygon method, boundary curvature, zipper method, geodesic algorithm, acoustic wave scattering, electro-magnetic wave scattering

  • 108.
    Andersson, Anders
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Numerical Conformal Mappings for Waveguides2010Inngår i: Computational Mathematics: Theory, Methods and Applications / [ed] Peter G. Chareton, Hauppauge, NY, USA: Nova Science Publishers, Inc., 2010Kapittel i bok, del av antologi (Annet vitenskapelig)
    Abstract [en]

    A number of newly developed numerical conformal mapping techniques are described. Their purpose is to achieve conformal mappings with good accuracy for regions bounded by smooth or piecewise smooth curves in which the boudary curve direction can be controllod, especially towards infinity in unbounded regions as for example waveguides.

    Most of the mappings are variants of the Schwarz-Christoffel mappings.

  • 109.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Numerical conformal mappings for waveguides2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with varying direction and cross-section can be re-formulated as a two-dimensional scattering problem, provided that the variations take place in only one dimension at a time. By using the so-called Building Block Method, it is possible to construct the scattering properties of a combination of scatterers when the properties of each scatterer are known. Hence, variations in the waveguide geometry or in the boundary conditions can be treated one at a time.

    Using the Building Block Method, the problem takes the form of the Helmholtz equation for stationary waves in a waveguide of infinite length and with smoothly varying geometry and boundary conditions. A conformal mapping is used to transform the problem into a corresponding problem in a straight horizontal waveguide, and by expanding the field in Fourier trigonometric series, the problem can be reformulated as an infinite-dimensional ordinary differential equation. From this, numerically solvable differential equations for the reflection and transmission operators are derived.

    To be applicable in the Building Block Method, the numerical conformal mapping must be constructed such that the direction of the boundary curve can be controlled. At the channel ends, it is an indispensable requirement, that the two boundary curves are (at least) asymptotically parallel and straight. Furthermore, to achieve bounded operators in the differential equations, the boundary curves must satisfy different regularity conditions, depending on the boundary conditions.

    In this work, several methods to accomplish such conformal mappings are presented. The Schwarz–Christoffel mapping, which is a natural starting point and for which also efficient numerical software exists, can be modified in different ways in order to achieve polygons with rounded corners. We present algorithms by which the parameters in the mappings can be determined after such modifications. We show also how the unmodified Schwarz–Christoffel mapping can be used for regions with a smooth boundary. This is done by constructing an appropriate outer polygon to the considered region.

    Finally, we introduce one method that is not Schwarz–Christoffel-related, by showing how one of the so-called zipper algorithms can be used for waveguides.

  • 110.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    On the curvature of an inner curve in a Schwarz-Christoffel mapping2007Rapport (Annet vitenskapelig)
    Abstract [en]

    In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-­Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded.

    In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-­Christoffel mapping from R, the unit disk or upper half­plane, to a polygonal region P of a curve inside R. From the Schwarz-­Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

  • 111.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Schwarz–Christoffel Mappings for Nonpolygonal Regions2008Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, nr 1, 94-111 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An approximate conformal mapping for an arbitrary region $\varOmega$ bounded by a smooth curve $\varGamma$ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which $\varOmega$ is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region $R$, approximately equal to $\varOmega$. $R$ is bounded by a $C^\infty$ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of $\Gamma$ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of $R$. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.

  • 112.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Schwarz-Christoffel Mappings for Nonpolygonal Regions2008Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, Vol. 31, nr 1, 94-111 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An approximate conformal mapping for an arbitrary region Ω bounded by a smooth curve Γ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which Ω is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region R, approximately equal to Ω. R is bounded by a C∞ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of Γ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of R. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.

  • 113.
    Andersson, Anders
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen. Matematik.
    Using a Zipper Algorithm to find a Conformal Map for a Channel with Smooth Boundary2006Inngår i: AIP Conference Proceedings: Second Conference on Mathematical Modeling of Wave Phenomena, American Institute of Physics, New York , 2006, 378- s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The so called geodesic algorithm, which is one of the zipper algorithms for conformal mappings, is combined with a Schwarz–Christoffel mapping, in its original or in a modified form, to produce a conformal mapping function between the upper half-plane and an arbitrary channel with smooth boundary and parallel walls at the end.

  • 114.
    Andersson, Anders
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Using a zipper algorithm to find a conformal map for a channel with smooth boundary2006Inngår i: Mathematical Modeling of Wave Phenomena: 2nd Conference, 2006, 378- s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The so called geodesic algorithm, which is one of the zipper algorithms for conformal mappings, is combined with a Schwarz–Christoffel mapping, in its original or in a modified form, to produce a conformal mapping function between the upper half-plane and an arbitrary channel with smooth boundary and parallel walls at the end.

  • 115.
    Andersson, Anders
    et al.
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Nilsson, Börje
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008Inngår i: International Conference on Numerical Analysis and Applied Mathematics 2008, AIP, Melville, USA , 2008, 33-36 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

  • 116.
    Andersson, Anders
    et al.
    Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
    Nilsson, Börje
    International Centre for Mathematical modelling, Växjö University.
    Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008Inngår i: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, 33-36 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

  • 117.
    Andersson, Anders
    et al.
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Nilsson, Börje
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Electro-Magnetic Scattering in Variously Shaped Waveguides with an Impedance Condition2009Inngår i: Mathematical modelling of wave phenomena: 3rd Conference on Mathematical Modelling of Wave Phenomena, Växjö, Sweden, 9 – 13 June 2008, Melville, New York: American Institute of Physics , 2009, 36-45 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

     

    Electro-magnetic scattering is studied in a waveguide with varying shape and crosssection. Furthermore, an impedance or admittance condition is applied to two of the waveguide walls. Under the condition that variations in geometry or impedance take place in only one plane at the time, the problem can be solved as a two-dimensional wave-scattering problems. By using newly developed numerical conformal mapping techniques, the problem is transformed into a wave-scattering problem in a straight two-dimensional channel. A numerically stable formulation is reached in terms of transmission and reflection operators. Numerical results are given for a slowly varying waveguide with a bend and for one more complex geometry.

     

  • 118.
    Andersson, Fredrik K.
    et al.
    WorldLight.com AB, Sweden.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    The mathematics of internet search engines2008Inngår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 104, nr 2, 211-242 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.

  • 119.
    Andersson Granberg, Tobias
    et al.
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Norin, Anna
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Värbrand, Peter
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Yuan, Di
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
    Integrating optimization and simulation to gain more efficient airport logistics2009Inngår i: Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009), 2009, 1-10 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper we present airport logistics, which is a framework of resource management in the air transportation system. Focus is on the processes supporting turn-around. A detailed simulation model of various processes involved in turn-around is developed, by which the interaction between these processes are analyzed. We show that integrating optimization and simulation is a powerful tool to demonstrate efficiency improvements in airport logistics, using scheduling de-icing trucks as an example. An optimization algorithm for scheduling de-icing trucks is developed and simulations are performed comparing different schedules. The schedule obtained when considering total airport performance in the optimization algorithm gives minimum flight delay and waiting times in the simulations.

  • 120.
    Andersson, Henrik
    Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska högskolan.
    Coordinated Routing: applications in location and inventory management2006Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Almost everywhere, routing plays an important role in everyday life. This thesis consists of three parts, each studying different applications where routing decisions are coordinated with other decisions. A common denominator in all applications is that an intelligent utilization of a fleet of vehicles is crucial for the performance of the system. In the first part, routing and inventorymanagement decisions are coordinated, in the second part, routing decisions concerning different modes of transportation are coordinated with inventory management, and in the third part, location decision and routing are coordinated.

    In the first part, an application concerning waste management is presented. Many industries generate garbage, and instead of handling the waste disposal themselves, other companies, specialized in garbage collection, handle the disposal. Each industry rents containers from a company to be used for waste, and the garbage collection companies handle the collection. The industries buy a service including one or more containers at the industry and the garbage collection companies are obliged to make sure that the containers never become overfull. The idea is that the industries buy this service and in return, the garbage collection company can plan the collection so that the overall cost and the number of overfull containers is minimized. Two models for the problem facing the garbage collection company are proposed. The first is solved using a Lagrangean relaxation approach on a flow based model, and the second is solved using Benders decomposition on a column based model.

    The second part investigates a distribution chain management problem taken from the Swedish pulp industry. Given fixed production plans at the mills, and fixed customer demands, the problem is to minimize the distribution cost. Unlike many other models for marine distribution chains, the customers are not located at the harbors. This means that the model proposed also incorporates the distribution planning from the harbors to the customers. All customers are not served from the harbors; some are served directly from the mills using trucks and trains to distribute the pulp, and these decisions are also included. The problem is modeled as a mixed integer linear program and solved using a branch and price scheme. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the vessels operated by the company, while the second deals with the chartering of vessels on the spot market.

    In the third part, routing is combined with location decisions in the location-routing problem. Special emphasis is given to strategic management where decision makers must make location, capacity and routing decisions over a long planning period. The studied application comes fromstrategic schoolmanagement, where the location and capacity of the schools as well as their catchment areas are under consideration. The problem is modeled as a mixed integer linear program. The computational study shows the importance of incorporating

    a routing component allowing multiple visits, as well as the danger of having a too short planning period.

  • 121.
    Andersson, Jerker
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Gymnasiematematik på distans: Varför så många avbryter sina distansstudier i matematik2006Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
    Abstract [sv]

    Syftet med studien är att undersöka varför det är så många distansstudenter som avbryter sina distansstudier i matematik. Distansutbildning (DU) är en studieform i stark frammarsch. Nyckelorden för en lyckad DU är bland annat flexibilitet och individanpassning. Medan flexibiliteten framförallt ökar tillgängligheten står individanpassningen som garant för en god lärsituation. Faktorer som i hög grad påverkar DU och genomströmningen är studiemotiv, artefakter och hur det sociala sammanhanget upplevs. Jag har i min undersökning samlat in data med hjälp av kvalitativa intervjuer och dessutom granskat distansupplägget som eleverna på den aktuella skolan haft. Urvalsgruppen består av fem stycken elever i olika åldersgrupper som redan klarat av halva kursen. Även analysen har skett med en kvalitativ ansats. I den aktuella studien kan man se att många av de riskfaktorer som tros ligga bakom många avhopp även föreligger här med det aktuella studieupplägget.

  • 122.
    Andersson, Joel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On the Theorem of Uniform Recovery of Random Sampling Matrices2014Inngår i: IEEE Transactions on Information Theory, ISSN 0018-9448, Vol. 60, nr 3, 1700-1710 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

  • 123.
    Andersson, Lars-Erik
    et al.
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016Inngår i: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, nr 1, 78-105 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 124.
    Andersson, Lennart
    et al.
    Luleå tekniska universitet.
    Grennberg, Anders
    Hedberg, Torbjörn
    Luleå tekniska universitet.
    Näslund, Reinhold
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Sydow, Björn von
    Luleå tekniska universitet.
    Söderkvist, Inge
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Linjär algebra med geometri1999Bok (Annet (populærvitenskap, debatt, mm))
  • 125.
    Andersson, Magnus
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Palm, Johan
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation.
    Forecasting the Stock Market: A Neural Network Approch2009Oppgave
    Abstract [en]

    Forecasting the stock market is a complex task, partly because of the random walk behavior of the stock price series. The task is further complicated by the noise, outliers and missing values that are common in financial time series. Despite of this, the subject receives a fair amount of attention, which probably can be attributed to the potential rewards that follows from being able to forecast the stock market.

    Since artificial neural networks are capable of exploiting non-linear relations in the data, they are suitable to use when forecasting the stock market. In addition to this, they are able to outperform the classic autoregressive linear models.

    The objective of this thesis is to investigate if the stock market can be forecasted, using the so called error correction neural network. This is accomplished through the development of a method aimed at finding the optimum forecast model.

    The results of this thesis indicates that the developed method can be applied successfully when forecasting the stock market. Of the five stocks that were forecasted in this thesis using forecast models based on the developed method, all generated positive returns. This suggests that the stock market can be forecasted using neural networks.

  • 126.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Rapport (Annet vitenskapelig)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

  • 127.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska högskolan.
    Global search strategies for solving multilinear least-squares problems2012Inngår i: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, nr 1, 12-21 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 128.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015Inngår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, nr 2, 259-277 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 129.
    Andersson, Mats
    et al.
    Linköpings universitet, Institutionen för medicinsk teknik. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Zikrin, Spartak
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska högskolan.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 130. Andersson, Paul
    et al.
    Berggren, Martin
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    Henningson, Dan S.
    Optimal disturbances and bypass transition in boundary layers1999Inngår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 11, 134-150 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 131.
    Andersson, Per-Åke
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [sv]

    I avhandlingen studeras hur kostnadseffektiva underhålls- (uh-)planer för belagd väg kan genereras, på basis av information om aktuellt vägytetillstånd och funktionella modeller för kostnads- och tillståndsförändringar, delvis utvecklade i samarbete med svenska Vägverket (VV). Tilltänkt användning är på strategisk och programnivå, innan mer detaljerad objektinformation finns att tillgå. Till skillnad från hittills använda modeller, så genereras individuella uh-planer för varje vägsegment (en homogen vägsträcka vad gäller aktuellt beläggningstillstånd och beläggningshistorik), i kontinuerliga tillstånds- och åtgärdsrum. Genom användning av Lagrangerelaxerande optimeringsteknik, så kan de speciella nytto/kostnads-kvot-villkor som VV ålägger varje uh-objekt naturligen hanteras med dualpriser för budgetvillkoren. Antalet vägsegment som konkurrerar om budgetmedlen är vanligtvis stort. Data från VV:s Vägdatabank för Värmland har använts, omfattande ca 9000 vägsegment. Genom den stora datamängden har datorprogrammen implementerats för parallellbearbetning. Under avhandlingsarbetet har projektet beviljats tillgång till Monolith PCklustret vid NSC. För att kunna reducera optimeringskörtiderna har modell- och metodutveckling varit nödvändig. Genom att aggregera vägsegmenten till vägklasser har goda startvärden på dualpriserna erhållits. Genom utvecklingen av en speciell restvärdesrutin har den explicit behandlade tidsperioden kunnat reduceras. Vid lösandet av det duala subproblemet har speciell uppmärksamhet ägnats åt de diskretiseringseffekter som uppstår i metoden dynamisk programmering. En typ av tillämpning avser ett delvägnät, exempelvis en väg. Valideringsstudier har genomförts på väg 63 i Värmland – med lovande men inte tillfredsställande resultat (se nedan). En speciell modell för samordnat uh beaktar stordriftsfördelarna vid samtidig åtgärd på en hel vägsträcka. Den andra huvudtypen av studier gäller ett helt nätverk. Flera metodtyper har tillämpats, både för att lösa de relaxerade optimeringsproblemen och för att generera uhplaner som uppfyller budgetvillkoren. För en anständig diskretisering är körtiderna för hela Värmland mindre än 80 CPU-timmar. Genom en a posteriori primal heuristik reduceras kraven på parallellbearbetning till ett litet PC-kluster. Avhandlingen studerar vidare effekterna av omfördelade budgetmedel samt en övergång till en transparent, stokastisk modell – vilka båda visar små avvikelser från basmodellen.

    Optimeringsresultaten för Värmland indikerar att budgetnivåer på ca 40% av Värmlands verkliga uh-budget är tillräckliga. Dock saknas viktiga kostnadsdrivande faktorer i denna första modellomgång, exempelvis vissa funktionella prestanda (säkerhet), all miljöpåverkande prestanda (buller etc.) och strukturell prestanda (ex.vis bärighet, som enbart modelleras via ett åldersmått). För ökad tilltro till PMS i allmänhet och optimering i synnerhet, bör avvikelserna analyseras ytterligare och leda till förbättringar vad gäller tillståndsmätning, tillståndseffekt- & kostnadsmodellering samt matematisk modellering & implementering.

  • 132.
    Andren, Daniel
    et al.
    Umeå University.
    Hellström, Lars
    Umeå University.
    Markström, Klas
    Umeå University.
    Fast multiplication of matrices over a finitely generated semiring2008Inngår i: Information Processing Letters, ISSN 0020-0190, E-ISSN 1872-6119, Vol. 107, nr 6, 230-234 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 133.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Adaptive Node Distribution for Online Trajectory PlanningManuskript (Annet vitenskapelig)
  • 134.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control2009Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

  • 135.
    Anisi, David A.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Online trajectory planning and observer based control2006Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.

    The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.

    Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.

    In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

    Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

  • 136.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hamberg, Johan
    Riemannian Observers for Euler-Lagrange Systems2005Inngår i: Proceedings of the 16th IFAC World Congress: Prague, Czech Republic, July 3-8, 2005, 2005, 115-120 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analysed. This observer is an generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contractivity is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. The convergence properties of the observer are illustrated by an example where the configuration manifold is the three-dimensional sphere, S3.

  • 137.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Active Observers for Mobile Robotic SystemsManuskript (Annet vitenskapelig)
    Abstract [en]

    An important class of non-uniformly observable systems come from applications in mobile robotics. In this paper, the problem of active observer design for such systems is considered. The set of feasible configurations and the set of output flow equivalent states is defined. It is shown that the inter-relation between these two sets serves as the basis for design of active observers. The proposed observer design method is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.

  • 138.
    Anisi, David A.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ögren, Petter
    Minimum time multi-UGV surveillance2008Inngår i: OPTIMIZATION AND COOPERATIVE CONTROL STRATEGIES / [ed] Hirsch MJ; Commander CW; Pardalos PM; Murphey R, Berlin: Springer Verlag , 2008, 31-45 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper addresses the problem of concurrent task- and path planning for a number of  surveillance Unmanned Ground Vehicles (UGVs) such that a user defined area of interest is covered by the UGVs' sensors in minimum time. We first formulate the problem, and show that it is in fact  a generalization of the Multiple Traveling Salesmen Problem (MTSP), which is known to be NP-hard. We then propose a solution that decomposes the problem into three subproblems. The first is to find a maximal convex covering of the search area. Most results on static coverage  use disjoint partitions of the search area, e.g. triangulation, to convert the continuous sensor positioning problem into a  discrete one. However, by a simple example, we show that a highly overlapping set of maximal convex sets is better suited for  minimum time coverage. The second subproblem is a combinatorial assignment and ordering of the sets in the cover.  Since Tabu search algorithms are known to perform well on various routing problems,  we use it as a part of our proposed solution. Finally, the third subproblem utilizes a particular shortest path sub-routine in order to find the vehicle paths, and calculate the overall objective function used in the Tabu search. The proposed algorithm is illustrated by a number of simulation examples.

  • 139. Anisi, David A.
    et al.
    Ögren, Petter
    Swedish Defence Research Agency (FOI), Sweden.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.
    Cooperative Minimum Time Surveillance With Multiple Ground Vehicles2010Inngår i: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, nr 12, 2679-2691 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we formulate and solve two different minimum time problems related to unmanned ground vehicle (UGV) surveillance. The first problem is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensors' field of view are assumed to have a limited coverage range and be occluded by the obstacles. The second problem extends the first by additionally requiring the induced information graph to be connected at the time instants when the UGVs perform the surveillance mission, i.e., when they gather and transmit sensor data. In the context of the second problem, we also introduce and utilize the notion of recurrent connectivity, which is a significantly more flexible connectivity constraint than, e.g., the 1-hop connectivity constraints and use it to discuss consensus filter convergence for the group of UGVs.

  • 140.
    Anisi, David
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Robinson, John W.C.
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Ögren, Petter
    Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
    Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task CompletionManuskript (Annet vitenskapelig)
    Abstract [en]

    On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order. 

  • 141.
    Ansanay-Alex, Guillaume
    et al.
    Institut de Sûreté et de Radioprotection Nucléaire.
    Babik, Fabrice
    Institut de Sûreté et de Radioprotection Nucléaire.
    Gastaldo, Laura
    Institut de Sûreté et de Radioprotection Nucléaire.
    Larcher, Aurélien
    Institut de Sûreté et de Radioprotection Nucléaire.
    Lapuerta, Céline
    Institut de Sûreté et de Radioprotection Nucléaire.
    Latché, Jean-Claude
    Institut de Sûreté et de Radioprotection Nucléaire.
    Vola, Didier
    Institut de Sûreté et de Radioprotection Nucléaire.
    A finite volume stability result for the convection operator in compressible flows. . . and some finite element applications2008Inngår i: Finite Volumes for Complex Applications V: Problems & Perspectives / [ed] Robert Eymard and Jean-Marc Hérard, Hermes Science Publications, 2008, 185-192 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    In this paper, we build a L2-stable discretization of the non-linear convection termin Navier-Stokes equations for non-divergence-free flows, for non-conforming low order Stokesfinite elements. This discrete operator is obtained by a finite volume technique, and its stability relies on a result interesting for its own sake: the L2-stability of the natural finite volume convection operator in compressible flows, under some compatibility condition with the discrete mass balance. Then, this analysis is used to derive a boundary condition to cope with physical situations where the velocity cannot be prescribed on inflow parts of the boundary of the computational domain. We finally collect these ingredients in a pressure correction scheme for low Mach number flows, and assess the capability of the resulting algorithm to compute a natural convection flow with artificial (open) boundaries.

  • 142.
    Antczak, Magdalena
    et al.
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Leniec, Marta
    Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), Tillämpad matematik och fysik (MPE-lab).
    Pricing and Hedging of Defaultable Models2011Independent thesis Advanced level (degree of Master (One Year)), 10 poäng / 15 hpOppgave
    Abstract [en]

    Modelling defaultable contingent claims has attracted a lot of interest in recent years, motivated in particular by the Late-2000s Financial Crisis. In several papers various approaches on the subject have been made. This thesis tries to summarize these results and derive explicit formulas for the prices of financial derivatives with credit risk. It is divided into two main parts. The first one is devoted to the well-known theory of modelling the default risk while the second one presents the results concerning pricing of the defaultable models that we obtained ourselves.

  • 143. Antolín, Roberto
    et al.
    Nettelblad, Carl
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Tillämpad beräkningsvetenskap. Uppsala universitet, Science for Life Laboratory, SciLifeLab.
    Gorjanc, Gregor
    Money, Daniel
    Hickey, John M.
    A hybrid method for the imputation of genomic data in livestock populations2017Inngår i: Genetics Selection Evolution, ISSN 0999-193X, E-ISSN 1297-9686, Vol. 49, 30Artikkel i tidsskrift (Fagfellevurdert)
  • 144.
    Antzutkin, Oleg
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Kota, Hanumantha Rao
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Ikumapayi, Fatai
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Holmgren, Allan
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Gunneriusson, Lars
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Johansson, Björn
    New Boliden AB.
    Berggren, Andreas
    New Boliden AB.
    Larsson, Anna-Carin
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Hedlund, Jonas
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Mouzon, Johanne
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Bhuiyan, Iftekhar Uddin
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Forsmo, Seija
    LKAB.
    Interactions in multi-component mineral systems2011Konferansepaper (Annet vitenskapelig)
  • 145.
    Antzutkin, Oleg
    et al.
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Kota, Hanumantha Rao
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Ikumapayi, Fatai
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Johansson, Björn
    New Boliden AB.
    Berggren, Andreas
    New Boliden AB.
    Larsson, Anna-Carin
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Holmgren, Allan
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Hedlund, Jonas
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Mouzon, Johanne
    Bhuiyan, Iftekhar Uddin
    Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Industriell miljö- och processteknik.
    Forsmo, Seija
    LKAB.
    Interactions in multi-component mineral systems2010Konferansepaper (Annet vitenskapelig)
  • 146. Anzt, Hartwig
    et al.
    Lukarski, Dimitar
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Tillämpad beräkningsvetenskap.
    Tomov, Stanimire
    Dongarra, Jack
    Self-adaptive multiprecision preconditioners on multicore and manycore architectures2015Inngår i: High Performance Computing for Computational Science – VECPAR 2014, Springer, 2015, 115-123 s.Konferansepaper (Fagfellevurdert)
  • 147.
    Aoki, Yasunori
    et al.
    Department of Applied Mathematics University of Waterloo 200 University Ave. West Waterloo N2L 3G1 Canada.
    De Sterck, Hans
    Numerical study of unbounded capillary surfaces2014Inngår i: Pacific Journal of Mathematics, ISSN 0030-8730, Vol. 267, nr 1, 1-34 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Unbounded capillary surfaces in domains with a sharp corner or a cusp are studied. It is shown how numerical study using a proposed computational methodology leads to two new conjectures for open problems on the asymptotic behavior of capillary surfaces in domains with a cusp. The numerical methodology contains two simple but important ingredients, a change of variable and a change of coordinates, which are inspired by known asymptotic approximations for unbounded capillary surfaces. These ingredients are combined with the finite volume element or Galerkin finite element methods. Extensive numerical tests show that the proposed computational methodology leads to a global approximation method for singular solutions of the Laplace–Young equation that recovers the proper asymptotic behavior at the singular point, is more accurate and has better convergence properties than numerical methods considered for singular capillary surfaces before. Using this computational methodology, two open problems on the asymptotic behavior of capillary surfaces in domains with a cusp are studied numerically, leading to two conjectures that may guide future analytical work on these open problems.

  • 148.
    Aoki, Yasunori
    et al.
    Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada.
    Hayami, Ken
    Res Org Informat & Syst, Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan.
    De Sterck, Hans
    Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada.
    Konagaya, Akihiko
    Tokyo Inst Technol, Midori Ku, Yokohama, Kanagawa 2268503, Japan.
    Cluster Newton Method for Sampling Multiple Solutions of Underdetermined Inverse Problems: Application to a Parameter Identification Problem in Pharmacokinetics2014Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 36, nr 1, B14-B44 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A new algorithm is proposed for simultaneously finding multiple solutions of an underdetermined inverse problem. The algorithm was developed for an ODE parameter identification problem in pharmacokinetics for which multiple solutions are of interest. The algorithm proceeds by computing a cluster of solutions simultaneously, and is more efficient than algorithms that compute multiple solutions one-by-one because it fits the Jacobian in a collective way using a least squares approach. It is demonstrated numerically that the algorithm finds accurate solutions that are suitably distributed, guided by a priori information on which part of the solution set is of interest, and that it does so much more efficiently than a baseline Levenberg-Marquardt method that computes solutions one-by-one. It is also demonstrated that the algorithm benefits from improved robustness due to an inherent smoothing provided by the least-squares fitting.

  • 149.
    Aoki, Yasunori
    et al.
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Farmaceutiska fakulteten, Institutionen för farmaceutisk biovetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
    Sundqvist, Monika
    AstraZeneca R&D.
    Hooker, Andrew C.
    Uppsala universitet, Medicinska och farmaceutiska vetenskapsområdet, Farmaceutiska fakulteten, Institutionen för farmaceutisk biovetenskap.
    Gennemark, Peter
    AstraZeneca R&D.
    PopED lite: an optimal design software for preclinical pharmacokinetic and pharmacodynamic studiesManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Optimal experimental design approaches are seldom used in pre-clinical drug discovery. Main reasons for this lack of use are that available software tools require relatively high insight in optimal design theory, and that the design-execution cycle of in vivo experiments is short, making time-consuming optimizations infeasible. We present the publicly available software PopED lite in order to increase the use of optimal design in pre-clinical drug discovery. PopED lite is designed to be simple, fast and intuitive. Simple, to give many users access to basic optimal design calculations. Fast, to fit the short design-execution cycle and allow interactive experimental design (test one design, discuss proposed design, test another design, etc). Intuitive, so that the input to and output from the software can easily be understood by users without knowledge of the theory of optimal design. In this way, PopED lite is highly useful in practice and complements existing tools. Key functionality of PopED lite is demonstrated by three case studies from real drug discovery projects. 

  • 150.
    Apelkrans, Mats Y. T.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för teknisk databehandling. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
    On difference schemes for hyperbolic equations with discontinuous initial values1968Inngår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 22, nr 103, 525-539 s.Artikkel i tidsskrift (Fagfellevurdert)
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