On the fundamental solutions-based inversion of Laplace matrices

Results in Applied Mathematics

C. Vuik¹  D.R. den Bakker²  F.J. Vermolen³ 

[1] Corresponding author at: University of Hasselt, Department of Mathematics and Statistics, Diepenbeek, Belgium.;Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands;University of Hasselt, Department of Mathematics and Statistics, Diepenbeek, Belgium;

关键词: Inverse matrix;    Laplace matrix;    Finite element discretisation;    Fundamental solutions;   

DOI  :  

来源: DOAJ

【 摘 要 】

The discretisation of the Laplacian results into the well-known Laplace matrix. In the case of a one dimensional problem, an explicit formula for its inverse is derived on the basis of fundamental solutions (Green’s functions) for general boundary conditions. For a linear reaction–diffusion equation, approximations of the inverse are given.

【 授权许可】

Unknown