Complete Eigenpairs of Hexagonal Seven-Point Laplacian in Fourier Vectors at Half-Integral Nodes

Abstract

Hexagonal grid methods are valuable in two-dimensional applications involving Laplacian. The methods are investigated on problems related to standard and anisotropic Laplacian using Fourier vectors in pure, mixed and combination types. Complete (positive) eigenvalues and eigenvectors are determined explicitly in terms of various bases in a unified structure. This work is the smallest completion of some previous works.