A Flexible, Parallel, Adaptive Geometric Multigrid Method for FEM
Thomas C. Clevenger, Timo Heister, Guido Kanschat, Martin Kronbichler
Abstract
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by using a space filling curve for the leaf mesh and distributing ancestors in the hierarchy based on the leaves. We present a model of the efficiency of mesh hierarchy distribution and compare its predictions to runtime measurements. The algorithm is implemented as part of the deal.II finite-element library and as such available to the public.
Topics & Concepts
Polygon meshMultigrid methodComputer scienceSmoothingHierarchyMassively parallelComputational scienceFinite element methodAlgorithmDistribution (mathematics)Mesh generationAdaptive mesh refinementMathematical optimizationApplied mathematicsSpace (punctuation)Parallel computingMathematicsComputational geometryNumerical analysisGeometric modelingDiscretizationAdvanced Numerical Methods in Computational MathematicsComputational Geometry and Mesh GenerationComputational Fluid Dynamics and Aerodynamics