Comparative study of multigrid methods and neural network methods for boundary value problems with irregular boundaries

In this paper multigrid methods and neural network methods were used to solve the partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated on two-dimensional and three-dimensional PDEs. According to the results, multigrid method seems to have certain advantages both in efficiency and in, interpolation accuracy.