Efficient interpolation strategies in multiscale multigrid computation

We introduce two new interpolation strategies, SOR strategy and rotated grid strategy, to compute the fine grid high order accurate solution in multiscale multigrid computation based on the Richardson extrapolation technique for solving partial differential equations. These new interpolation strategies effectively accelerate or eliminate the iterative refinement process previously employed in multiscale multigrid computation to obtain high order accurate solution on the fine grid. Experimental results show that the proposed new interpolation strategies are much more efficient and faster than the previously used iterative refinement strategy to compute high order accurate solution on the fine grid.