On the fundamental solutions-based inversion of Laplace matrices

F.J. Vermolen, D.R. Bakker, C. Vuik

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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.
Original languageEnglish
Article number100288
Number of pages12
JournalResults in Applied Mathematics
Volume15
DOIs
Publication statusPublished - 2022

Keywords

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

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