A kernel-free boundary integral method for elliptic PDEs on a doubly connected domain View Full Text


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Article Info

DATE

2022-08-17

AUTHORS

Yue Cao, Yaning Xie, Mahesh Krishnamurthy, Shuwang Li, Wenjun Ying

ABSTRACT

We present a kernel-free boundary integral method (KFBIM) for solving variable coefficients partial differential equations (PDEs) in a doubly connected domain. We focus our study on boundary value problems (BVP) and interface problems. A unique feature of the KFBIM is that the method does not require an analytical form of the Green’s function for designing quadratures but rather computes boundary or volume integrals by solving an equivalent interface problem on Cartesian mesh. We first decompose the problem defined in a doubly connected into two separate interface problems. The system of boundary integral equations is solved using the Krylov method. The method is second-order accurate in space, and its complexity is linearly proportional to the number of mesh points. Numerical examples demonstrate that the method is robust for variable coefficients PDEs, even for cases with large diffusion coefficients ratio and complex geometries where two interfaces are close. More... »

PAGES

2

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URI

http://scigraph.springernature.com/pub.10.1007/s10665-022-10233-8

DOI

http://dx.doi.org/10.1007/s10665-022-10233-8

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