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When attempting to solve partial differential equations (PDEs), we often look to discrete numerical methods. These methods often lead to the need to efficiently solve a large linear system. To do this, we chose to use a multigrid solver. An important part of multigrid is the relaxation of oscillatory errors in the approximation of the solution. There are cases in which traditional smoothers such ... read moreas Jacobi or Gauss-Seidel methods either perform exceedingly poorly or completely fail altogether. We consider solving the Stokes equations and Maxwell's equations using the Finite Element and the Finite Difference method, respectively. In these cases, we use a block-overlapping type smoother coupled with a multigrid solver. The results for the constant coefficient case show that this is an effective choice.read less
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