Meshing method to build a centrosymmetric matrix to solve partial differential equations on an irreducible domain including a planar symmetry

Abstract

A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both the domain to solve and the boundary condition (BC) type accept a planar symmetry, while no conditions are required on the BC values and the PDE right hand size function. It is applicable to finite element or finite difference method (FDM). It relies both on the specific construction of a mesh having a planar symmetry and a centrosymmetric numbering of the mesh nodes used to solve the PDE on the domain. The method is exemplified with a simple PDE using FDM. The method allows to reduce the numerical problem size to solve by a factor of two, decreasing as much the computing time and the need of computer memory.