A Fast Spectral Subtractional Solver for Elliptic Equations

Authors:
Elena Braverman;Boris Epstein;Moshe Israeli;Amir Averbuch
Affiliations:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada. maelena@math.ucalgary.ca;The Academic College of Tel Aviv-Yaffo, Antokolsky Str. 4, Tel Aviv 64044, Israel;Technion-Israel Institute of Technology, Computer Science Department, Haifa 32000, Israel;School of Computer Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Journal of Scientific Computing
Year:
2004

Citing 16
Cited 3

Spectral method solution of the Stokes equations on nonstaggered grids

Journal of Computational Physics
Spectral multidomain technique with local Fourier basis

Journal of Scientific Computing
A fast Poisson solver for complex geometries

Journal of Computational Physics
A direct adaptive Poisson solver of arbitrary order accuracy

Journal of Computational Physics
A spectral embedding method applied to the advection-diffusion equation

Journal of Computational Physics
Unsteady Two-Dimensional Flows in Complex Geometries: Comparative Bifurcation Studies with Global Eigenfunction Expansions

SIAM Journal on Scientific Computing
On the Gibbs Phenomenon and Its Resolution

SIAM Review
A Fast Poisson Solver of Arbitrary Order Accuracy in Rectangular Regions

SIAM Journal on Scientific Computing
On a high order numerical method for functions with singularities

Mathematics of Computation
A fast 3D Poisson solver of arbitrary order accuracy

Journal of Computational Physics
Efficient pseudospectral flow simulations in moderately complex geometries

Journal of Computational Physics
A Fast Spectral Solver for a 3D Helmholtz Equation

SIAM Journal on Scientific Computing
Mixed spectral-boundary element embedding algorithms for the Navier-Stokes equations in the vorticity-stream function formulation

Journal of Computational Physics
A direct spectral collocation Poisson solver in polar and cylindrical coordinates

Journal of Computational Physics
A Hierarchical 3-D Poisson Modified Fourier Solver by Domain Decomposition

Journal of Scientific Computing
A Modified Fourier–Galerkin Method for the Poisson and Helmholtz Equations

Journal of Scientific Computing

An accurate Fourier-spectral solver for variable coefficient elliptic equations

ISTASC'05 Proceedings of the 5th WSEAS/IASME International Conference on Systems Theory and Scientific Computation
High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm

Journal of Computational Physics
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square

Journal of Scientific Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

The paper presents a fast subtractional spectral algorithm for the solution of the Poisson equation and the Helmholtz equation which does not require an extension of the original domain. It takes O(N2 log N) operations, where N is the number of collocation points in each direction. The method is based on the eigenfunction expansion of the right hand side with integration and the successive solution of the corresponding homogeneous equation using Modified Fourier Method. Both the right hand side and the boundary conditions are not assumed to have any periodicity properties. This algorithm is used as a preconditioner for the iterative solution of elliptic equations with non-constant coefficients. The procedure enjoys the following properties: fast convergence and high accuracy even when the computation employs a small number of collocation points. We also apply the basic solver to the solution of the Poisson equation in complex geometries.