A kernel-free boundary integral method for elliptic PDEs on a doubly connected domain
A kernel-free boundary integral method for elliptic PDEs on a doubly connected domain
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DOI：
10.1007/s10665-022-10233-8
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发表时间：
2022-08
影响因子：
1.3
通讯作者：
Yue Cao;Yaning Xie;M. Krishnamurthy;Shuwang Li;W. Ying
中科院分区：
文献类型：
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作者：
Yue Cao;Yaning Xie;M. Krishnamurthy;Shuwang Li;W. Ying
提出了一种求解双连通区域上变系数偏微分方程的无核边界积分方法。我们的研究重点是边值问题和界面问题。KFBIM的一个独特之处是，该方法不需要设计求积的绿色函数的解析形式，而是通过求解笛卡尔网格上的等效界面问题来计算边界或体积积分。我们首先将定义在双连通域中的问题分解为两个独立的接口问题.边界积分方程的系统使用Krylov方法求解。该方法在空间上具有二阶精度，其复杂度与网格点数成线性关系。数值算例表明，该方法是强大的变系数偏微分方程，即使是大的扩散系数比和复杂的几何形状，两个界面接近的情况下。
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.