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arXiv · 1902.03713

The Smooth Selection Embedding Method with Chebyshev Polynomials

Daniel Agress·Patrick Guidotti·Dong Yan
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Abstract

We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by recasting them as constrained optimization problems in a simple encompassing set. Previously, the SSEM was introduced and implemented using a periodic box (read a torus) using Fourier series; here, it is implemented on a (non-periodic) rectangle using Chebyshev polynomial expansions. This implementation has faster convergence on smaller grids. Numerical experiments will demonstrate that the method provides a simple, robust, efficient, and high order fictitious domain method which can solve problems in complex geometries, with non-constant coefficients, and for general boundary conditions.

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Daniel Agress, Patrick Guidotti, Dong Yan. 2019-02-11. The Smooth Selection Embedding Method with Chebyshev Polynomials. https://arxiv.org/abs/1902.03713

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