Inexact solvers on element interfaces for the p and h- p finite element method

Abstract

Parallel and iterative solvers for large-scale linear system arising from finite element discretization, based on domain decomposition, decompose the approximation spaces into a number of subspaces. The corresponding subproblems are solved in these subspaces, and the solutions are corrected in an iterative process. The subproblems are much smaller in size and much easier to be solved. One of these subspaces is spanned by (high order) element side modes in two dimensions and (high order) element face modes in three dimensions. Solving the subproblems on the element interfaces is a major cost in each step of iteration. To reduce computational cost, various inexact solvers on element interfaces are proposed in this paper, with theoretical analysis and numerical illustrations.