Journal of Computational Physics
Spectral domain embedding for elliptic PDEs in complex domains
Journal of Computational and Applied Mathematics
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations
Journal of Computational Physics
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
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In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions. The idea is to embed the domain into a box and use a smoothing term to encode the boundary conditions into a modified equation that can be approached by standard spectral methods. The main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via fast Fourier transform routines. We discuss several examples of practical interest and test the results against standard numerical methods.