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Spektralmetoder för linjära elliptiska partiella differentialekvationer i fri rymd
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Spectral methods for linear elliptic partial differential equations in free space (English)
Abstract [sv]

Syftet med den här studien är att lösa linjära elliptiska partiella differentialek- vationer i fri rymd och att uppnå spektralkonvergenta numeriska lösningar, för glatta och kompakt stödda inhomogeniteter i två och tre dimensioner. Detta utförs genom att använda teori om Greenfunktioner och göra en om- skrivning av differentialoperatorns Greenfunktion i fri rymd till en trunkerad spektralrepresentation, genom att nyttja inhomogenitetens kompakta stöd; därefter, genom att använda resultat från Fourieranalysen och egenskaper av faltning, beräknas lösningen med hjälp av en snabb Fouriertransform. Trots att partiella differentialekvationer ofta kräver icke-triviala lösningsmetoder, resulterar detta kraftfulla tillvägagångssätt i ett simpelt och snabbt sätt att uppnå spektralkonvergenta numeriska lösningar.

 

Abstract [en]

The purpose of this study is to solve linear elliptic partial differential equa- tions in free space and to achieve spectrally accurate numerical solutions, for smooth and compactly supported inhomogeneities in two and three dimen- sions. This is made by using results from theory of Green’s functions and rewriting the differential operator’s free space Green’s function to a trun- cated spectral representation, by utilizing the inhomogeneity’s compact sup- port; then, using results from Fourier analysis and properties of convolution, calculations are performed using a fast Fourier transform. Although partial differential equations often require non trivial solution methods, this pow- erful approach results in a simple and fast way of achieving highly accurate numerical solutions.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:173
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254796OAI: oai:DiVA.org:kth-254796DiVA, id: diva2:1335368
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Examiners
Available from: 2019-07-05 Created: 2019-07-05 Last updated: 2019-07-05Bibliographically approved

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