Finite Element Monte-carlo Algorithm For A Class Of Elliptic Boundary Value Problems

In the fields of physics and engineering technology,we often encounter such numerical simulation problems: accurately numerically simulate the strain,stress and displacement of partial differential equations at certain special points.such as centralized load problem is such a kind of problem.For this kind of problem,using the finite element method directly requires more storage space and computation time.In this paper,a numerical algorithm for numerical simulation of the function value of elliptic problem at any point is proposed based on the finite element method.In this paper,the numerical simulation algorithm of function values at any point is studied for a class of singular elliptic boundary value problems.Here are the specific tasks:Firstly,using the solution technique of Green function,we make a comprehensive and in-depth study on the numerical simulation algorithmof the function value of singular elliptic problem in two-dimensional second order at any point based on the finite element method.At the same time,we use numerical examples to test the effectiveness and advanced nature of the proposed algorithm.Then,using the solution technique of green function,we make a comprehensive and in-depth study on the numerical simulation algorithm of the function value of the second order with singularity of high dimension(dimension greater than or equal to 3)based on the finite element method.Finally,this paper makes a plan and thinking on the future research.The work of this paper is of great significance to the numerical simulation of mechanical problems.