An EXCMG accelerated multiscale multigrid computation for 3D Poisson equation

Multiscale multigrid (MSMG) method is an effective computational framework for efficiently computing high accuracy solutions for elliptic partial differential equations. In the current MSMG method, compared to the CPU cost on computing sixth-order solutions by applying extrapolation and other techniques on two fourth-order solutions from different scales grids, much more CPU time is spent on computing fourth-order solutions themselves on coarse and fine grids, particularly for high-dimensional problems. Here we propose to embed extrapolation cascadic multigrid (EXCMG) method into the MSMG framework to accelerate the whole process. Numerical results on 3D Poisson equations show that the new EXCMG–MSMG method is more efficient than the existing MSMG method and the EXCMG method for sixth-order solution computation.