Isogeometric Schwarz preconditioners for linear elasticity systems

DOI10.1016/j.cma.2012.10.011zbMath1297.74113OpenAlexW2091515911MaRDI QIDQ465819

Durkbin Cho, Lourenco Beirão da Veiga, Luca F. Pavarino, Simone Scacchi

Publication date: 24 October 2014

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2012.10.011

zbMATH Keywords

linear elasticitymixed methodsisogeometric analysisalmost incompressible materialsoverlapping Schwarzscalable domain decomposition preconditioners

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Uses Software

• GeoPDEs
• IETI

Cites Work

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• \textsc{GeoPDEs}: a research tool for isogeometric analysis of PDEs
• Anisotropic NURBS approximation in isogeometric analysis
• Isogeometric analysis and domain decomposition methods
• The cost of continuity: a study of the performance of isogeometric finite elements using direct solvers
• Multigrid methods for isogeometric discretization
• IETI -- isogeometric tearing and interconnecting
• Some estimates for \(h\)-\(p\)-\(k\)-refinement in isogeometric analysis
• Isogeometric analysis in electromagnetics: B-splines approximation
• Isogeometric analysis using T-splines
• Isogeometric shell analysis: the Reissner-Mindlin shell
• Efficient quadrature for NURBS-based isogeometric analysis
• The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations
• Robustness of isogeometric structural discretizations under severe mesh distortion
• \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
• Isogeometric analysis using T-splines on two-patch geometries
• Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
• Isogeometric fluid-structure interaction: Theory, algorithms, and computations
• A fully ``locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Isogeometric analysis of structural vibrations
• Studies of refinement and continuity in isogeometric structural analysis
• Indefinite overlapping Schwarz methods for time-dependent Stokes problems
• Overlapping Schwarz methods for mixed linear elasticity and Stokes problems
• Overlapping Schwarz and spectral element methods for linear elasticity and elastic waves
• Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with \(k\)-method NURBS
• BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS
• Overlapping Schwarz Methods for Isogeometric Analysis
• ISOGEOMETRIC COLLOCATION METHODS
• Isogeometric Discrete Differential Forms in Three Dimensions
• A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
• Overlapping Schwarz Methods for Fekete and Gauss–Lobatto Spectral Elements
• An Overlapping Schwarz Algorithm for Almost Incompressible Elasticity
• Mixed and Hybrid Finite Element Methods
• Domain Decomposition Algorithms with Small Overlap
• Isogeometric Analysis
• Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique
• Spectral Methods
• The Mathematical Theory of Finite Element Methods
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES