Abstract:In this report, I will introduce the semi-group formulation of the SPDE. And I shall give a stability analysis for filtering algorithm based on spectral methods from two aspects.1. Asymptotic analysis of the relationship between the number of spectra and errors in spectral methods.2. Analysis of the stability of spectral algorithm by time discretization
摘 要:An important problem in numerical analysis is the solution of the Helmholtz equation in exerior domains, in variable media; this models the scattering of time-harmonic waves. The Finite Element Method (FEM) is a flexible and powerful tool for obtaining numerical solutions, but difficulties are known to arise in obtaining convergence estimates for FEM that are uniform as the frequency of ...