NDLI: Efficient MFS Algorithms for Inhomogeneous Polyharmonic Problems

Content Provider	Springer Nature Link
Author	Karageorghis, A.
Copyright Year	2010
Abstract	In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ$^{ℓ}$ u=f, ℓ∈ℕ, in circular geometries. Following the ideas of Alves and Chen (Adv. Comput. Math. 23:125–142, 2005), the right hand side of the equation in question is approximated by a linear combination of fundamental solutions of the Helmholtz equation. A particular solution of the inhomogeneous equation is then easily obtained from this approximation and the resulting homogeneous problem in the method of particular solutions is subsequently solved using the method of fundamental solutions. The fact that both the problem of approximating the right hand side and the homogeneous boundary value problem are performed in a circular geometry, makes it possible to develop efficient matrix decomposition algorithms with fast Fourier transforms for their solution. The efficacy of the method is demonstrated on several test problems.
Starting Page	519
Ending Page	541
Page Count	23
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	46
Issue Number	3
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2010-09-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Method of fundamental solutions Polyharmonic equations Circulant matrices Fast Fourier transforms Theoretical, Mathematical and Computational Physics ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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