Quasi Multigrid Preconditioned Iteration Method Of Two-dimensional Partial Differential Equation Problems

Aiming at the problem of the numerical solution of the two-dimensional partial differential equation problems, preconditioning method and multigrid method are combined together, taking the advantages of preconditioning matrix reducing the condition numbers of preconditioning method and the fast convergence speed of multigrid method, we construct to solve Quasi Multigrid Preconditioned Iteration Method for Boundary Value Problem of two-dimensional Elliptic Equations, using five point difference format and rotating five point difference format to discretize, this paper gives the form of iterative matrix and sets up the corresponding algorithm, using numerical examples to compare it with SOR Method and verifies its effectiveness and feasibility. Quasi multigrid preconditioned iteration method for boundary value problem is extended to quasi multigrid preconditioned iteration method for initial boundary value problem of two-dimensional parabolic equations of numerical solution further, gives the form of transition matrix and iterative matrix and the corresponding algorithm. The result shows that, Quasi multigrid preconditioned iteration method greatly reduces the workload of the numerical solution of two-dimensional partial differential equation problems and the convergence speed increases remarkably, thereby this paper verifies the superiority of preconditioning method and multigrid method.