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
A Fast Spectral Subtractional Solver for Elliptic Equations
Journal of Scientific Computing
International Journal of High Performance Computing Applications
High order accurate particular solutions of the biharmonic equation on general regions
Contemporary mathematics
PHLST5: A Practical and Improved Version of Polyharmonic Local Sine Transform
Journal of Mathematical Imaging and Vision
Linear Image Reconstruction by Sobolev Norms on the Bounded Domain
International Journal of Computer Vision
Harmonic Wavelet Transform and Image Approximation
Journal of Mathematical Imaging and Vision
Periodic Plus Smooth Image Decomposition
Journal of Mathematical Imaging and Vision
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In this paper we propose a direct method for the solution of the Poisson equation in rectangular regions. It has an arbitrary order accuracy and low CPU requirements which makes it practical for treating large-scale problems.The method is based on a pseudospectral Fourier approximation and a polynomial subtraction technique. Fast convergence of the Fourier series is achieved by removing the discontinuities at the corner points using polynomial subtraction functions. These functions have the same discontinuities at the corner points as the sought solution. In addition to this, they satisfy the Laplace equation so that the subtraction procedure does not generate nonperiodic, nonhomogeneous terms. The solution of a boundary value problem is obtained in a series form in O(N log N) floating point operations, where N2 is the number of grid nodes. Evaluating the solution at all N2 interior points requires O(N2 log N) operations.