On the fundamental solutions-based inversion of Laplace matrices

Vermolen, F.J.; Bakker, D.R.; Vuik, Cornelis

doi:10.1016/j.rinam.2022.100288

On the fundamental solutions-based inversion of Laplace matrices

Title

On the fundamental solutions-based inversion of Laplace matrices

Author

Vermolen, F.J. (TU Delft Numerical Analysis; University of Hasselt)
Bakker, D.R. (Student TU Delft)
Vuik, Cornelis (TU Delft Delft Institute of Applied Mathematics)

Date

2022

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.

Subject

Inverse matrix
Laplace matrix
Finite element discretisation
Fundamental solutions

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http://resolver.tudelft.nl/uuid:fce4b6af-ac6b-4601-bb5c-843a0062491a

DOI

https://doi.org/10.1016/j.rinam.2022.100288

ISSN

2590-0374

Source

Results in Applied Mathematics, 15

Part of collection

Institutional Repository