A Mixed Basis Perturbation Approach to Approximate the Spectrum of Laplace Operator

2009/09/04 by Nordin, Matias, Nilsson-Jacobi, Martin, Nydén, Magnus
#Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.0909.0935

Abstract

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. The method is applied to several 2 dimensional geometries with Neumann boundary conditions.

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