Robust and scalable domain decomposition solvers for unfitted finite element methods

DOI10.1016/j.cam.2017.09.034zbMath1462.65216arXiv1703.06323OpenAlexW2612209730MaRDI QIDQ724567

Francesc Verdugo, Santiago Badia

Publication date: 26 July 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06323

zbMATH Keywords

domain decompositionparallel computingembedded boundary methodslinear solversunfitted finite elements

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (15)

Mixed Aggregated Finite Element Methods for the Unfitted Discretization of the Stokes Problem ⋮ Numerical analysis of interface hybrid difference methods for elliptic interface equations ⋮ Multigrid solvers for immersed finite element methods and immersed isogeometric analysis ⋮ Distributed-memory parallelization of the aggregated unfitted finite element method ⋮ Convergence of H(div)-conforming schemes for a new model of sedimentation in circular clarifiers with a rotating rake ⋮ A tutorial-driven introduction to the parallel finite element library \texttt{FEMPAR} V1.0.0 ⋮ Preconditioning immersed isogeometric finite element methods with application to flow problems ⋮ Hierarchical multigrid approaches for the finite cell method on uniform and multi-level \(h p\)-refined grids ⋮ A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics ⋮ \texttt{FEMPAR}: an object-oriented parallel finite element framework ⋮ A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems ⋮ Linking ghost penalty and aggregated unfitted methods ⋮ Dual fat boundary method: the fat boundary method in elasticity with an extension of the application scope ⋮ The Aggregated Unfitted Finite Element Method on Parallel Tree-Based Adaptive Meshes ⋮ Robust high-order unfitted finite elements by interpolation-based discrete extension

Uses Software

• METIS
• ParMETIS
• BDDC
• CutFEM
• PCBDDC
• FEMPAR

Cites Work

• Unnamed Item
• The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models
• Implementation and scalability analysis of balancing domain decomposition methods
• An adaptive choice of primal constraints for BDDC domain decomposition algorithms
• Fluid-structure partitioned procedures based on Robin transmission conditions
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients
• An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves
• Condition number analysis and preconditioning of the finite cell method
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Arbitrary discontinuities in finite elements
• PCBDDC: A Class of Robust Dual-Primal Methods in PETSc
• BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS
• A Highly Scalable Parallel Implementation of Balancing Domain Decomposition by Constraints
• Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods
• A Quasi-algebraic Multigrid Approach to Fracture Problems Based on Extended Finite Elements
• FETI-DP Methods with an Adaptive Coarse Space
• Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry
• CutFEM: Discretizing geometry and partial differential equations
• A robust preconditioning technique for the extended finite element method
• Encyclopedia of Parallel Computing
• Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations
• Multilevel Balancing Domain Decomposition at Extreme Scales
• A Preconditioner for Substructuring Based on Constrained Energy Minimization
• Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
• Mesh adaptation for Dirichlet flow control via Nitsche's method
• Convergence of a balancing domain decomposition by constraints and energy minimization

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