摘要
This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface problems.The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations.Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution,which satisfies an equivalent discrete interface problem,while the interface problem is solved by a fast solver in the Cartesian grid.The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain.This paper gives implementation details for a secondorder version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems.The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem,where the elliptic PDEs on two sides of the interface are of different types.
基金
supported in part by the National Science Foundation of the USA under Grant DMS-0915023
is supported by the National Natural Science Foundation of China under Grants DMS-11101278 and DMS-91130012
supported by the Young Thousand Talents Program of China
supported in part by National Science Committee of Taiwan under Grant 99-2115-M-007-002-MY2
supported in part by National Center for Theoretical Sciences of Taiwan,too.
