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科学计算与偏微分方程数值解近展Recent Advances on Scientific Computing and Numerical PDEs小型研讨会

A robust multilevel preconditioner for the Helmholtz equation

Speaker

Xuejun Xu , 同济大学/中科院数学与系统科学研究院

Time

12 Dec, 09:30 - 10:10

Abstract

In this talk, we shall present a robust multilevel preconditioner for the algebraic system resulting from the continuous interior penalty finite element method for the approximation of the Helmholtz equation. The key idea in this work is the replacement of traditional smoothers by the one level overlapping domain decomposition method on coarse grids. The proposed multilevel method then serves as a preconditioner in the outer GMRES iteration. Numerical results show that for fixed wave numbers, the convergence of our multilevel method is independent of the mesh size. Furthermore, the performance of the algorithm depends mildly on the wave number.