A kernel-free boundary integral method for elliptic interface problems on surfaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918128930258944 |
|---|---|
| author | Yin, Pengsong YIng, Wenjun Zhang, Yulin Zhou, Han |
| author_facet | Yin, Pengsong YIng, Wenjun Zhang, Yulin Zhou, Han |
| contents | This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel function is not required when solving the boundary integral equations. The numerical integration of single- and double-layer potentials or volume integrals at the boundary is replaced by interpolation of the solution to an equivalent interface problem, which is then solved using a fast multigrid solver on Cartesian grids. This paper provides detailed implementation of the second-order version of the kernel-free boundary integral method for elliptic PDEs defined on an embedding surface in $\mathbb{R}^3$ and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A kernel-free boundary integral method for elliptic interface problems on surfaces Yin, Pengsong YIng, Wenjun Zhang, Yulin Zhou, Han Numerical Analysis 65N06, 35R01, 35J25 This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel function is not required when solving the boundary integral equations. The numerical integration of single- and double-layer potentials or volume integrals at the boundary is replaced by interpolation of the solution to an equivalent interface problem, which is then solved using a fast multigrid solver on Cartesian grids. This paper provides detailed implementation of the second-order version of the kernel-free boundary integral method for elliptic PDEs defined on an embedding surface in $\mathbb{R}^3$ and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems. |
| title | A kernel-free boundary integral method for elliptic interface problems on surfaces |
| topic | Numerical Analysis 65N06, 35R01, 35J25 |
| url | https://arxiv.org/abs/2508.16061 |