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Parallelization of the multi-level \(hp\)-adaptive finite cell method. (English) Zbl 1375.65151
Summary: The multi-level \(hp\)-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes, a \(hp\)-scheme based on spatial refinement by superposition. An efficient parallelization of this method using standard domain decomposition approaches in combination with ghost elements faces the challenge of a large basis function support resulting from the overlay structure and is in many cases not feasible. In this contribution, a parallelization strategy for the multi-level \(hp\)-scheme is presented that is adapted to the scheme’s simple hierarchical structure. By distributing the computational domain among processes on the granularity of the active leaf elements and utilizing shared mesh data structures, good parallel performance is achieved, as redundant computations on ghost elements are avoided. We show the scheme’s parallel scalability for problems with a few hundred elements per process. Furthermore, the scheme is used in conjunction with the finite cell method to perform numerical simulations on domains of complex shape.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
65Y20 Complexity and performance of numerical algorithms
35J25 Boundary value problems for second-order elliptic equations
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