Bq. Guo et Wm. Cao, INEXACT SOLVERS ON ELEMENT INTERFACES FOR THE P-FINITE-ELEMENT AND H-P-FINITE-ELEMENT METHOD, Computer methods in applied mechanics and engineering, 150(1-4), 1997, pp. 173-189
Parallel and iterative solvers for large-scale linear system arising f
rom finite element discretization, based on domain decomposition, deco
mpose the approximation spaces into a number of subspaces. The corresp
onding subproblems are solved in these subspaces, and the solutions ar
e corrected in an iterative process. The subproblems are much smaller
in size and much easier to be solved. One of these subspaces is spanne
d by (high order) element side modes in two dimensions and (high order
) element face modes in three dimensions. Solving the subproblems on t
he element interfaces is a major cost in each step of iteration. To re
duce computational cost, various inexact solvers on element interfaces
are proposed in this paper, with theoretical analysis and numerical i
llustrations.