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.

翻译：本文提出了一种通用方法，通过线性方程组生成与不可约域上偏微分方程求解相关的中心对称矩阵。该方法适用于任何满足以下条件的偏微分方程：求解域和边界条件类型均允许平面对称性，而对边界条件值和偏微分方程右端函数无特殊要求。该方法可应用于有限元法或有限差分法。其核心在于构建具有平面对称性的特定网格，并对用于求解域上偏微分方程的网格节点进行中心对称编号。本文通过一个使用有限差分法的简单偏微分方程示例演示了该方法。该方法可将待求解数值问题的规模减半，从而显著降低计算时间和计算机内存需求。