A Fast Cartesian Grid-Based Integral Equation Method for Unbounded Interface Problems with Non-Homogeneous Source Terms  

作　　者：Jiahe Yang Wenjun Ying 

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Minhang,Shanghai 200240,P.R.China [2]Department of Mathematics,MOE-LSC and Institute of Natural Sciences,Shanghai Jiao Tong University,Minhang,Shanghai 200240,P.R.China

出　　处：《Communications in Computational Physics》2023年第6期208-234,共27页计算物理通讯（英文）

基　　金：supported by the National Key R&D Program of China(Project No.2020YFA0712000);supported by the Shanghai Science and Technology Innovation Action Plan in Basic Research Area(Project No.22JC1401700);the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25010405);the National Natural Science Foundation of China(Grant No.DMS-11771290).

摘　　要：This work presents a fast Cartesian grid-based integral equation method for unbounded interface problems with non-homogeneous source terms.The unbounded interface problem is solved with boundary integral equation methods such that infinite boundary conditions are satisfied naturally.This work overcomes two difficulties.The first difficulty is the evaluation of singular integrals.Boundary and volume integrals are transformed into equivalent but much simpler bounded interface problems on rectangular domains,which are solved with FFT-based finite difference solvers.The second one is the expensive computational cost for volume integrals.Despite the use of efficient interface problem solvers,the evaluation for volume integrals is still expensive due to the evaluation of boundary conditions for the simple interface problem.The problem is alleviated by introducing an auxiliary circle as a bridge to indirectly evaluate boundary conditions.Since solving boundary integral equations on a circular boundary is so accurate,one only needs to select a fixed number of points for the discretization of the circle to reduce the computational cost.Numerical examples are presented to demonstrate the efficiency and the second-order accuracy of the proposed numerical method.

关 键 词：Interface problem unbounded domain boundary integral equation kernel-free method auxiliary circle Cartesian grid method fast algorithm 

分 类 号：O17[理学—数学]