报告人：Liu Jijun教授
东南大学
报告时间：2022年11月6日（星期日）
报告地点：ZOOM: 813 1612 3284， Password：221106
报告摘要：
For the boundary value problems of linear elliptic system with variable coefficients, the finite element method (FEM) schemes are standard and efficient. Motivated by the surface potential representation of the solution for the linear elliptic equation with constant coefficients, which is of great importance in the researches of inverse problems where the adjoint operators are required in the iteration process, we establish a linear integral system for finding the solution to an elliptic equation with variable coefficients under the framework of the Levi function, which provides an alternative way for solving inverse problems in inhomogeneous media. The well-posedness of this integral system with respect to the density functions to be determined is rigorously proved. To solve the integral system numerically, except for the singularity decomposition for the Levi function, we proposed an adaptive discretization scheme for computing the integrals with continuous integrands, which leads to the unform accuracy of the integral in the whole domain, and consequently the efficient computations for the density functions. The numerical realizations of the proposed scheme are presented.