On fast Fourier solvers for the tensor product high-order FEM for a generalized Poisson equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866912798329536512 |
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| author | Zlotnik, Alexander Zlotnik, Ilya |
| author_facet | Zlotnik, Alexander Zlotnik, Ilya |
| contents | We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They are based on the well-known Fourier approaches. The key new points are the fast direct and inverse FFT-based algorithms for expansion in eigenvectors of the 1D eigenvalue problems for the high order FEM. The algorithms can further be used for numerous applications, in particular, to implement the tensor product high order finite element methods for various time-dependent PDEs. Results of numerical experiments in 2D and 3D cases are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_03967 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On fast Fourier solvers for the tensor product high-order FEM for a generalized Poisson equation Zlotnik, Alexander Zlotnik, Ilya Numerical Analysis 65F05, 65F15, 65M60, 65T99 We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They are based on the well-known Fourier approaches. The key new points are the fast direct and inverse FFT-based algorithms for expansion in eigenvectors of the 1D eigenvalue problems for the high order FEM. The algorithms can further be used for numerous applications, in particular, to implement the tensor product high order finite element methods for various time-dependent PDEs. Results of numerical experiments in 2D and 3D cases are presented. |
| title | On fast Fourier solvers for the tensor product high-order FEM for a generalized Poisson equation |
| topic | Numerical Analysis 65F05, 65F15, 65M60, 65T99 |
| url | https://arxiv.org/abs/1701.03967 |