Multiscale generalized FEMs with wavenumber explicit convergence analysis for heterogeneous Helmholtz equations
Multiscale generalized FEMs with wavenumber explicit convergence analysis for heterogeneous Helmholtz equations
报告人：马楚鹏（海德堡大学应用数学研究所）
报告时间： 11月30日15:00-16:00
腾讯会议ID：136 527 541
摘要：In this talk, a generalized finite element method with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is discussed. The local spaces are built from selected eigenvectors of local eigenvalue problems defined on generalized harmonic spaces. At both continuous and discrete levels, (i) wavenumber explicit and nearly exponential decay rates for the local approximation errors are obtained without any assumption on the size of subdomains; (ii) a quasi-optimal and nearly exponential global convergence rate of the method is established by assuming that the size of subdomains is O(1/k) (k is the wavenumber). The method at the continuous level extends the plane wave partition of unity method to the heterogeneous-coefficients case, and at the discrete level, it delivers an efficient non-iterative domain decomposition method for solving discrete Helmholtz problems resulting from standard FE discretizations. Numerical results are provided to confirm the theoretical analysis and to validate the proposed method.
报告人简介：马楚鹏，2017年博士毕业于中国科学院大学数学与系统科学研究院，目前为海德堡大学应用数学研究所博士后。主要研究方向为偏微分方程数值分析与多尺度数值方法。
邀请人：卢培培