Distributed-memory parallelization of the aggregated unfitted finite element method

Abstract

The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitted, or extended finite element methods. The method is based on removal of basis functions associated with badly cut cells by introducing carefully designed constraints, which results in well-posed systems of linear algebraic equations, while preserving the optimal approximation order of the underlying finite element spaces. The specific goal of this work is to present the implementation and performance of the method on distributed-memory platforms aiming at the efficient solution of large-scale problems. In particular, we show that, by considering AgFEM, the resulting systems of linear algebraic equations can be effectively solved using standard algebraic multigrid preconditioners. This is in contrast with previous works that consider highly customized preconditioners in order to allow one the usage of iterative solvers in combination with unfitted techniques. Another novelty with respect to the methods available in the literature is the problem sizes that can be handled with the proposed approach. While most of previous references discussing linear solvers for unfitted methods are based on serial non-scalable algorithms, we propose a parallel distributed-memory method able to efficiently solve problems at large scales. This is demonstrated by means of a weak scaling test defined on complex 3D domains up to 300M degrees of freedom and one billion cells on 16K CPU cores in the Marenostrum-IV platform. The parallel implementation of the AgFEM method is available in the large-scale finite element package FEMPAR.

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• Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids
• Geometrical discretisations for unfitted finite elements on explicit boundary representations
• A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics
• High order unfitted finite element discretizations for explicit boundary representations
• A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0
• A three-grid high-order immersed finite element method for the analysis of CAD models
• Space-time unfitted finite elements on moving explicit geometry representations
• Unfitted finite element interpolated neural networks