Signal reconstruction for the diffusion transport equation using tensorial spline Galerkin approximation

被引：5

作者：

Addam, M. ^{[1
]}

Bouhamidi, A. ^{[1
]}

Jbilou, K. ^{[1
]}

机构：

[1] Univ Lille Nord France, ULCO, LMPA, F-62228 Calais, France

来源：

APPLIED NUMERICAL MATHEMATICS | 2012年 / 62卷 / 09期

关键词：

Parabolic diffusion equation; Robin boundary conditions; Fourier transform; Galerkin method; Tensorial spline functions; Gauss-Hermite quadrature; Interpolation; Error estimate; Numerical analysis; SCATTERING;

D O I：

10.1016/j.apnum.2011.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the deterministic transport problem with Robin boundary conditions in optically diffusion medium. Existence and uniqueness for the such elliptic equation are given. An approximation of the photon density in frequency-domain is proposed by using a Galerkin method based on the tensorial B-splines. We propose the Gauss-Hermite quadrature formulation for the computation of the inverse Fourier transform of the temporal signal. This technique allows us to avoid the use of a method such as finite difference method. Error estimates are studied and some numerical examples are given. (c) 2011 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1089 / 1108

页数：20