Gisela Pöplau
Fast Solvers for Elliptic PDE's with Radial Basis Functions
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs

65N15 Error bounds for boundary value problems involving PDEs

41A63 Multidimensional problems

Abstract:
We construct fast direct solvers for elliptic partial differential equations by means
of radial basis functions using the concept of shift-invariant subspaces. Applying
the 'periodic' Strang-Fix conditions for radial basis functions, this method provides
error estimates with explicit constants. Numerical algorithms using FFT techniques
are presented and the error caused by the algorithms is estimated. Numerical
examples for the 2- and 3- dimensional case confirm the theoretical results.


Keywords: Fast direct solvers, radial basis functions, shift-invariant periodic subspaces, Strang-Fix conditions, FFT, embedding problem