Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Spectral multidomain technique with local Fourier basis
Journal of Scientific Computing
Multidomain local Fourier method for PDEs in complex geometries
Proceedings of the 6th international congress on Computational and applied mathematics
A spectral embedding method applied to the advection-diffusion equation
Journal of Computational Physics
Spectrally Accurate Solution of Nonperiodic Differential Equations by the Fourier--Gegenbauer Method
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Computational Physics
A direct spectral method for determination of flows over corrugated boundaries
Journal of Computational Physics
On Some Applications of the Superposition Principle with Fourier Basis
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Pseudospectral Fourier reconstruction with the modified Inverse Polynomial Reconstruction Method
Journal of Computational Physics
Computers & Mathematics with Applications
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
On the Fourier Extension of Nonperiodic Functions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
Journal of Computational Physics
A Fast Algorithm for Fourier Continuation
SIAM Journal on Scientific Computing
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
Approximation error in regularized SVD-based Fourier continuations
Applied Numerical Mathematics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Spatially Dispersionless, Unconditionally Stable FC---AD Solvers for Variable-Coefficient PDEs
Journal of Scientific Computing
Hi-index | 31.49 |
The range of Fourier methods can be significantly increased by extending a nonperiodic function f(x) to a periodic function f̃ on a larger interval. When f(x) is analytically known on the extended interval, the extension is straightforward. When f(x) is unknown outside the physical interval, there is no standard recipe. Worse still, like a radarless aircraft groping through fog, the algorithm may wreck on the "mountain-in-fog" problem: a function f(x) which is perfectly well behaved on the physical interval may very well have singularities in the extended domain. In this article, we compare several algorithms for successfully extending a function f(x) into the "fog" even when the analytic extension is singular. The best third-kind extension requires singular value decomposition with iterative refinement but achieves accuracy close to machine precision.