Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains

Details Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains

2007-08-27

arxiv.org/abs/0708.3533v1

Mathematics

Numerical Analysis

25 pages, 14 figures, submitted to J. Comp. Phys

Scientific paper

10.1016/j.jcp.2008.04.008

The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary value problems. Its main drawback is that it often leads to ill-conditioned systems of equations. In this paper we investigate for the interior Helmholtz problem on analytic domains how the singularities (charge points) of the MFS basis functions have to be chosen such that approximate solutions can be represented by the MFS basis in a numerically stable way. For Helmholtz problems on the unit disc we give a full analysis which includes the high frequency (short wavelength) limit. For more difficult and nonconvex domains such as crescents we demonstrate how the right choice of charge points is connected to how far into the complex plane the solution of the boundary value problem can be analytically continued, which in turn depends on both domain shape and boundary data. Using this we develop a recipe for locating charge points which allows us to reach error norms of typically 10^{-11} on a wide variety of analytic domains. At high frequencies of order only 3 points per wavelength are needed, which compares very favorably to boundary integral methods.

Affiliated with

Also associated with

No associations

Rating

Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability and convergence of the Method of Fundamental Solutions for Helmholtz problems on analytic domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-125965