EVENTO
Pollution free Difference Schemes for Helmholtz Equation
Tipo de evento: Seminário LNCC
This is a joint work with Kun Wang & Jian DengThe Helmholtz equation arises in many problems related to wave propagations, such as acoustic, electromagnetic wave scattering and models in geophysical applications. Developing efficient and highly accurate numerical schemes to solve the Helmholtz equation at large wave numbers is a very challenging scientific problem and it has attracted a great deal of attention for a long time. The foremost difficulty in solving the Helmholtz equation is to eliminate or minimize the pollution effect which could lead to a serious problem as the wave number increases. Let k, h, and n denote the wave number, the grid size and the order of a finite difference or finite element approximations, we could show that the relative error is bounded by where or 1 for a finite difference or finite element method. In this talk, we present a new approach to construct difference schemes for one-dimensional Helmholtz equation with constant wave numbers, and it is shown that error estimate is bounded by and the convergence is independent of the wave number k even when kh >1. In the second part, we extend the idea on constructing the pollution free difference schemes to multi-dimensional Helmholtz equation in the polar and spherical coordinates. The superior performances of the new schemes are validated by comparing the numerical solutions with those obtained by the standard finite difference and the fourth-order compact schemes.
Data Início: 16/04/2015 Hora: 14:00 Data Fim: Hora: 15:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Yau Shu Wong - University of Alberta - -
