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Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Method of Moments is a numerical technique for solving electromagnetic problems with integral equations. The method discretizes a surface in three dimensions, which reduces the dimension of the problem with one. A drawback of the method is that it yields a dense system of linear equations. This effectively prohibits the solution of large scale problems.

Papers I-III describe the Fast Multipole Method. It reduces the cost of computing a dense matrix vector multiplication. This implies that large scale problems can be solved on personal computers. In Paper I the error introduced by the Fast Multipole Method is analyzed. Paper II and Paper III describe the implementation of the Fast Multipole Method.

The problem of computing monostatic Radar Cross Section involves many right hand sides. Since the Fast Multipole Method computes a matrix times a vector, iterative techniques are used to solve the linear systems. It is important that the solution time for each system is as low as possible. Otherwise the total solution time becomes too large. Different techniques for reducing the work in the iterative solver are described in Paper IV-VI. Paper IV describes a block Quasi Minimal Residual method for several right hand sides and Sparse Approximate Inverse preconditioner that reduce the number of iterations significantly. In Paper V and Paper VI a method based on linear algebra called the Minimal Residual Interpolation method is described. It reduces the work in an iterative solver by accurately computing an initial guess for the iterative method.

In Paper VII a hybrid method between Physical Optics and the Fast Multipole Method is described. It can handle large problems that are out of reach for the Fast Multipole Method.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2003. , p. 38
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 916
Keywords [en]
Fast Multipole Method, Minimal Residual Interpolation, Sparse Approximate Inverse preconditioning, Method of Moments, fast solvers, iterative methods, multiple right-hand sides, error analysis
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-3884ISBN: 91-554-5827-0 (print)OAI: oai:DiVA.org:uu-3884DiVA, id: diva2:163813
Public defence
2004-01-30, Room 1211, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2003-12-09 Created: 2003-12-09 Last updated: 2011-10-26Bibliographically approved
List of papers
1. Stability of the High Frequency Fast Multipole Method for Helmholtz’ Equation in Three Dimensions
Open this publication in new window or tab >>Stability of the High Frequency Fast Multipole Method for Helmholtz’ Equation in Three Dimensions
2004 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 44, p. 773-791Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71125 (URN)10.1007/s10543-004-4412-8 (DOI)
Projects
GEMS
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2018-01-10Bibliographically approved
2. A fast multipole method solver for large scale scattering problems
Open this publication in new window or tab >>A fast multipole method solver for large scale scattering problems
2001 (English)In: Proc. EMB 01, Electromagnetic Computations: Methods and Applications, Uppsala, Sweden: Division of Scientific Computing, Uppsala University , 2001, p. 148-155Conference paper, Published paper (Other academic)
Place, publisher, year, edition, pages
Uppsala, Sweden: Division of Scientific Computing, Uppsala University, 2001
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71134 (URN)91-631-1629-4 (ISBN)
Projects
GEMS
Available from: 2007-02-03 Created: 2007-02-03 Last updated: 2018-01-10Bibliographically approved
3. A Parallel Shared Memory Implementation of the Fast Multipole Method for Electromagnetics
Open this publication in new window or tab >>A Parallel Shared Memory Implementation of the Fast Multipole Method for Electromagnetics
2003 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2003-049
National Category
Computer Sciences Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-49030 (URN)
Projects
GEMS
Available from: 2007-02-13 Created: 2007-02-13 Last updated: 2018-01-11Bibliographically approved
4. A fast multipole accelerated block quasi minimum residual method for solving scattering from perfectly conducting bodies
Open this publication in new window or tab >>A fast multipole accelerated block quasi minimum residual method for solving scattering from perfectly conducting bodies
2000 (English)In: Proc, IEEE , 2000, p. 1848-1851Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
IEEE, 2000
Series
Antennas and Propagation Society International Symposium ; 2000:4
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71136 (URN)10.1109/APS.2000.874848 (DOI)0-7803-6369-8 (ISBN)
Projects
GEMS
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-10Bibliographically approved
5. A minimal residual interpolation method for linear equations with multiple right-hand sides
Open this publication in new window or tab >>A minimal residual interpolation method for linear equations with multiple right-hand sides
2004 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 25, p. 2126-2144Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71122 (URN)10.1137/S106482750241877X (DOI)
Projects
GEMS
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2018-01-10Bibliographically approved
6. Rapid solution of parameter-dependent linear systems for electromagnetic problems in the frequency domain
Open this publication in new window or tab >>Rapid solution of parameter-dependent linear systems for electromagnetic problems in the frequency domain
2005 (English)In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 53, p. 777-784Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71127 (URN)10.1109/TAP.2004.841293 (DOI)
Projects
GEMS
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2018-01-10Bibliographically approved
7. The minimum residual interpolation method applied to multiple scattering in MM-PO
Open this publication in new window or tab >>The minimum residual interpolation method applied to multiple scattering in MM-PO
2003 (English)In: Proc, IEEE , 2003, p. 828-831Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
IEEE, 2003
Series
Antennas and Propagation Society International Symposium ; 2003:3
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-71132 (URN)10.1109/APS.2003.1220038 (DOI)0-7803-7846-6 (ISBN)
Projects
GEMS
Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2018-01-10Bibliographically approved

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