The Composite Grid Method for Singular Problems of Partial Differential Equations

Abstract

Partial differential equations are crucial in scientific computing, and this paper will consider some of the problems of partial differential equation singularities. The Composite Mesh Method (CGM) is a new and improved numerical method for solving partial differential equations based on existing numerical methods for finite elements. The method has two meshes over the entire domain—a coarse and a fine set. The two sets of meshes generated by Mesh3 are separate in their respective regions and do not nest or interact. This method improves the accuracy of solving the numerical solution of partial differential equations. This paper discusses the CGM method based on the Finite Element Program Generator (FEPG) and uses it to simulate several singular problems. The numerical simulation results show that the proposed method can obtain more satisfactory simulation results for global problems and use a smaller number of computational generations than the general finite element method.

Keywords

• partial differential equations
• composite grid method
• finite element method
• numerical simulation