Theoretical Study Of Meshless Method And Its Application In Helmholtz Equation And Cancer Cell Diffusion Equation

The meshless method is a node-based approximation,which can completely or partially eliminate the mesh,and overcomes the deficiency that the finite element method needs to pre-mesh the mesh when forming the function approximation.The element-free Galerkin method is a new numerical calculation method that has emerged in the past decade.This method does not need to divide cells and meshes when processing data,which simplifies some data processing and improves in some aspects.The calculation speed can be solved,and some problems that cannot be solved by the finite element method can be solved.First,in the first chapter of this paper,the development of meshless method and the research status at home and abroad are introduced in detail,and the Helmholtz equation and cancer cell diffusion equation are briefly introduced.Secondly,in Chapter 2,the basic theory and approximation methods of the meshless method are described in detail,and the basic process and basic method of processing the equations are introduced in detail.Finally,the element-free Galerkin method is studied in Chapters 3 and 4.The element-free Galerkin method is generally used for numerical analysis of solid mechanics.Here we will use the element-free Galerkin method to perform discrete and numerical simulations of Helmholtz equation and cancer cell diffusion equation.Numerical examples verify the numerical accuracy of the method for two types of partial differential equations.And compared with other methods.It can be seen that this method has good adaptability.It is applicable to Helmholtz problem and cancer cell proliferation problem,and has a good application prospect.