Two Dimensional Fourier Continuation for Domains with Corners
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908990221320192 |
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| author | Bruno, Oscar P. Yang, Allen |
| author_facet | Bruno, Oscar P. Yang, Allen |
| contents | This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over general two-dimensional (2D) domains, including domains with corners. The algorithm operates with an O(N log N) computational cost, for an N-point discretization grid, and it achieves a user-prescribed d-th order of accuracy. The methodology can be generalized to non-smooth domains of arbitrary dimensionality, but such extensions are not considered in the present work. The usefulness and performance of the 2D-FC method are demonstrated through applications to the Poisson problem posed on bounded 2D domains with corners. One illustrative application concerns a Poisson problem on a non-smooth drop-shaped domain with a highly oscillatory forcing term; employing a discretization containing approximately four million degrees of freedom, the method produces the Poisson solution with accuracies of the order of machine precision in computing times on the order of one second on a single core of a present-day computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two Dimensional Fourier Continuation for Domains with Corners Bruno, Oscar P. Yang, Allen Numerical Analysis 65N35, 65T40, 35J05 This paper presents a fast "two-dimensional Fourier Continuation" (2D-FC) method for the construction of biperiodic extensions of smooth, non-periodic functions defined over general two-dimensional (2D) domains, including domains with corners. The algorithm operates with an O(N log N) computational cost, for an N-point discretization grid, and it achieves a user-prescribed d-th order of accuracy. The methodology can be generalized to non-smooth domains of arbitrary dimensionality, but such extensions are not considered in the present work. The usefulness and performance of the 2D-FC method are demonstrated through applications to the Poisson problem posed on bounded 2D domains with corners. One illustrative application concerns a Poisson problem on a non-smooth drop-shaped domain with a highly oscillatory forcing term; employing a discretization containing approximately four million degrees of freedom, the method produces the Poisson solution with accuracies of the order of machine precision in computing times on the order of one second on a single core of a present-day computer. |
| title | Two Dimensional Fourier Continuation for Domains with Corners |
| topic | Numerical Analysis 65N35, 65T40, 35J05 |
| url | https://arxiv.org/abs/2604.22111 |