On the fundamental solutions-based inversion of Laplace matrices

Abstract

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.

Keywords

• Inverse matrix
• Laplace matrix
• Finite element discretisation
• Fundamental solutions