The aggregated unfitted finite element method on parallel tree-based adaptive meshes. (English) Zbl 1472.65141
In this paper the authors built a bridge between the parallel adaptive tree-based meshing and the robust and scalable aggregated finite element method (AgFEM) as an unfitted FEM. The mathematical analysis of AgFEM has been detailed in a previous paper of authors and in this paper they are mainly concerned with the optimal error-driven \(h\)-adaptivity of this method in practical large-scale FEM applications. Actually a discrete extension operator from well-posed to ill-posed DOFs is constructed as AgFEM is based on it. Some numerical experiments concerning a non homogeneous Dirichlet boundary value problem for 2D and 3D Poisson equation on some non trivial domains are carried out. From mathematical point of view the paper contains two useful appendices. In the first one the authors built up the AgFEM space and in the second they prove that both the condition number of the mass matrix associated to the AgFEM space and of the linear system involved are bounded.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 65Y20 | Complexity and performance of numerical algorithms |
Keywords:
unfitted finite elements; algebraic multigrid; adaptive mesh refinement; nontrivial domain; forest of trees; high performance scientific computingReferences:
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