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
A Fast Spectral Solver for a 3D Helmholtz Equation
SIAM Journal on Scientific Computing
A Fast Spectral Subtractional Solver for Elliptic 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
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In this paper we present a modified Fourier–Galerkin method for the numerical solution of the Poisson and Helmholtz equations in a d-dimensional box. The inversion of the differential operators requires O(Nd) operations, where Nd is the number of unknowns. The total cost of the presented algorithms is O(Nd log2 N), due to the application of the Fast Fourier Transform (FFT) at the preprocessing stage. The method is based on an extension of the Fourier spaces by adding appropriate functions. Utilizing suitable bilinear forms, approximate projections onto these extended spaces give rapidly converging and highly accurate series expansions.