题 目：Wave-number-explicit analysis for maxwell's equation with Dirichlet-to-Neumann truncation
主讲人：江雪 教授
单 位：北京工业大学
时 间：2026年1月21日 15:20
地 点：九章学堂南楼C座302
摘 要：This work is focused on the propagation of electromagnetic waves in R^3 described by Maxwell's equation with large wave number and Silver-Muller radiation condition. The model problem is approximated by truncating the exact Dirichlet-to-Neumann (DtN) operator into a finite sum of vector spherical harmonics. We prove the well-posedness and wave-number-explicit H(curl)- stability of the solution to truncated problem by assuming that the truncation number N satisfies NkR for some > 1, where k represents the wave number and R is the radius of the physical domain. Additionally, we demonstrate that the truncated solution is exponentially close, in terms of N, to the true scattering solution. Finally, we present the hp-finite element method (hp-FEM) for the truncated problem, along with its asymptotic error estimate. Some numerical experiments are provided to validate the theoretical findings.
