Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Yin, Pengsong, YIng, Wenjun, Zhang, Yulin, Zhou, Han
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077674401
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