Accelerating the convergence of algebraic multigrid for quadratic finite element method by introducing grid information and p-multigrid

This paper proposes a new multigrid method for quadratic finite element method(FEM) by introducing mesh information and p-multigrid. The first level coarse grid is constructed geometrically; the first level restriction and prolongation matrices are built according to the relation of the local basis functions of quadratic and linear FEM. Then, traditional algebraic multigrid(AMG) method is applied to the linear FE problem rather than the original algebraic system. For the tested case, the proposed method only needs about 60% iterations and CPU time of traditional AMG to achieve same accuracy.