FETI-DP: a dual-primal unified FETI method?part I: A faster alternative to the two-level FETI method
From MaRDI portal
Publication:2709672
DOI10.1002/nme.76zbMath1008.74076OpenAlexW1971812145MaRDI QIDQ2709672
Le Tallec, Patrick, Charbel Farhat, Michel Lesoinne, Daniel J. Rixen, Kendall H. Pierson
Publication date: 10 April 2003
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.76
Lagrange multipliersiterative methodsFETI methoddual-primal formulationscalable domain decomposition methodstwo-level extension FETI-2
Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
Software concepts and numerical algorithms for a scalable adaptive parallel finite element method, Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner, Agile structural analysis for fabrication-aware shape editing, A scalable multiscale LATIN method adapted to nonsmooth discrete media, Scalable preconditioning for the stabilized contact mechanics problem, IETI-DP methods for discontinuous Galerkin multi-patch isogeometric analysis with T-junctions, Scalable total BETI based algorithm for 3D coercive contact problems of linear elastostatics, BDDC and FETI-DP algorithms with a change of basis formulation on adaptive primal constraints, Parallel iterative substructuring in structural mechanics, A BDDC algorithm for a class of staggered discontinuous Galerkin methods, Positive definite balancing Neumann-Neumann preconditioners for nearly incompressible elasticity, A TFETI domain decomposition solver for elastoplastic problems, Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings, Stress-aware large-scale mesh editing using a domain-decomposed multigrid solver, Non-intrusive coupling: recent advances and scalable nonlinear domain decomposition, A one-level FETI method for the drift-diffusion-Poisson system with discontinuities at an interface, On the spectrum of Schur complements of 2D elastic clusters joined by rigid edge modes and hybrid domain decomposition, On the mechanical modeling of anisotropic biological soft tissue and iterative parallel solution strategies, The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures, Large-scale parallel topology optimization using a dual-primal substructuring solver, Accelerating the convergence of AFETI partitioned analysis of heterogeneous structural dynamical systems, A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff-Love shells, A posteriori estimates for a natural Neumann-Neumann domain decomposition algorithm on a unilateral contact problem, A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models, Dense granular dynamics analysis by a domain decomposition approach, Mechanism free domain decomposition, On large-scale generalized inverses in solving two-by-two block linear systems, A practical factorization of a Schur complement for PDE-constrained distributed optimal control, A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, BDDC and FETI-DP preconditioners with adaptive coarse spaces for three-dimensional elliptic problems with oscillatory and high contrast coefficients, BDDC and FETI-DP for the virtual element method, On the selection of primal unknowns for a FETI-DP formulation of the Stokes problem in two dimensions, Cholesky decomposition of a positive semidefinite matrix with known kernel, Variational theory and domain decomposition for nonlocal problems, A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces, A hybrid discontinuous Galerkin method for computing the ground state solution of Bose-Einstein condensates, An adaptive BDDC method enhanced with prior selected primal constraints, On the initial estimate of interface forces in FETI methods., An extension of the FETI domain decomposition method for incompressible and nearly incompressible problems., The mosaic of high performance domain decomposition methods for structural mechanics: formulation, interrelation and numerical efficiency of primal and dual methods., A numerical study on Neumann-Neumann and FETI methods for \(hp\) approximations on geometrically refined boundary layer meshes in two dimensions., Partitioned formulation of internal and gravity waves interacting with flexible structures, The FETI family of domain decomposition methods for inequality-constrained quadratic programming: application to contact problems with conforming and nonconforming interfaces, Partitioned treatment of uncertainty in coupled domain problems: a separated representation approach, The derived-vector space framework and four general purposes massively parallel DDM algorithms, Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains, Preconditioned iteration for saddle-point systems with bound constraints arising in contact problems, Parallel computation approaches for flexible multibody dynamics simulations, High performance simulations of electrokinetic flow and transport in microfluidic chips, A continuous framework for FETI-DP with a mesh independent condition number for the dual problem, Asynchronous multi-domain variational integrators for nonlinear hyperelastic solids, A domain decomposition method for problems with structural heterogeneities on the interface: application to a passenger ship, A frugal FETI-DP and BDDC coarse space for heterogeneous problems, A preconditioner for the FETI-DP method for mortar-type Crouzeix-Raviart element discretization., A deluxe FETI-DP preconditioner for a composite finite element and DG method, IETI -- isogeometric tearing and interconnecting, BDDC algorithms for advection-diffusion problems with HDG discretizations, Adaptive FETI-DP and BDDC methods with a generalized transformation of basis for heterogeneous problems, Non-overlapping domain decomposition solution schemes for structural mechanics isogeometric analysis, A strongly coupled model reduction of vibro-acoustic interaction, A non-invasive implementation of a mixed domain decomposition method for frictional contact problems, Theoretically supported scalable BETI method for variational inequalities, A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains, Concurrent multiscale modeling of microstructural effects on localization behavior in finite deformation solid mechanics, Application of the parallel BDDC preconditioner to the Stokes flow, Overlapping and non-overlapping domain decomposition methods for large-scale meshless EFG simulations, A two-level nonoverlapping Schwarz algorithm for the Stokes problem: numerical study, Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems, Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions, An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics, An algebraic theory for primal and dual substructuring methods by constraints, Iterative solvers for coupled fluid-solid scattering, A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface, FETI based algorithms for contact problems: Scalability, large displacements and 3D Coulomb friction, Analysis of problems in elasto-plasticity via an adaptive FEM-BEM coupling method, A preconditioned dual-primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations, Analysis of FETI methods for multiscale PDEs, Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability, Multispace and multilevel BDDC, A FETI method with a mesh independent condition number for the iteration matrix, Coarse spaces for FETI-DP and BDDC methods for heterogeneous problems: connections of deflation and a generalized transformation-of-basis approach, Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations, FETI-DP, An enhanced nonlinear multi-scale strategy for the simulation of buckling and delamination on 3D composite plates, Non-overlapping domain decomposition methods in structural mechanics, Non-intrusive and exact global/local techniques for structural problems with local plasticity, Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems, Incorporation of linear multipoint constraints in domain-decomposition-based iterative solvers. II: Blending FETI-DP and mortar methods and assembling floating substructures, A scalable FETI-DP algorithm for a semi-coercive variational inequality, BDDC and FETI-DP preconditioners for spectral element discretizations, Adaptive selection of face coarse degrees of freedom in the BDDC and the FETI-DP iterative substructuring methods, Robust FETI-DP methods for heterogeneous three dimensional elasticity problems, On the use of inexact subdomain solvers for BDDC algorithms, BDDC and FETI-DP without matrices or vectors, On a mixed and multiscale domain decomposition method, Scalable and robust dual-primal Newton-Krylov deluxe solvers for cardiac electrophysiology with biophysical ionic models, Globalization of nonlinear FETI-DP domain decomposition methods using an SQP approach, Newton-Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model, An iterative substructuring method for coupled fluid-solid acoustic problems, On the performance of domain decomposition methods for modeling heterogenous materials, BDDC and FETI-DP Methods with Enriched Coarse Spaces for Elliptic Problems with Oscillatory and High Contrast Coefficients, Newton-Krylov-FETI-DP with Adaptive Coarse Spaces, New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables, Treatment of Singular Matrices in the Hybrid Total FETI Method, Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media, Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch IgA, A comparative study of scalable multilevel preconditioners for cardiac mechanics, Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review, Inexact and primal multilevel FETI‐DP methods: a multilevel extension and interplay with BDDC, Displacement‐based partitioned equations of motion for structures: Formulation and proof‐of‐concept applications, Challenges of order reduction techniques for problems involving polymorphic uncertainty, Implementation of balancing domain decomposition method for parallel finite element analysis involving inactive elements, On the use of graph centralities to compute generalized inverse of singular finite element operators: Applications to the analysis of floating substructures, The Schwarz alternating method for transient solid dynamics, A generalized elastic coordinate method for unconstrained structural dynamics, Asynchronous multisplitting-based primal Schur method, A coupled FETI-BDNM for solving 3D elastic frictional contact problem, A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations, Isogeometric tearing and interconnecting solvers for linear elasticity in multi-patch isogeometric analysis with theory for two dimensional domains, Non-overlapping domain decomposition algorithms with only primal velocity unknowns for the discontinuous viscosity Stokes problem, A Matrix-Free ILU Realization Based on Surrogates, Learning adaptive coarse basis functions of FETI-DP, Data-driven Whitney forms for structure-preserving control volume analysis, Robust and efficient FETI domain decomposition algorithms for edge element approximations, DUAL-PRIMAL METHODS FOR THE CARDIAC BIDOMAIN MODEL, Balancing Domain Decomposition by Constraints and Perturbation, A Parallel Solver for Large Scale DFN Flow Simulations, A Deflation Based Coarse Space in Dual-Primal FETI Methods for Almost Incompressible Elasticity, Extended preconditioners for the FETI method applied to constrained problems, Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure, Deflated preconditioned conjugate gradient solvers for linear elasticity, A two-level nonoverlapping Schwarz algorithm for the Stokes problem without primal pressure unknowns, A dual-primal FETI method for solving a class of fluid-structure interaction problems in the frequency domain, A simple explicit-implicit finite element tearing and interconnecting transient analysis algorithm, A fast block low-rank dense solver with applications to finite-element matrices, Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method, Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics, Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations, Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems, Parallel Newton--Krylov BDDC and FETI-DP Deluxe Solvers for Implicit Time discretizations of the Cardiac Bidomain Equations, Isogeometric BDDC deluxe preconditioners for linear elasticity, Numerical analysis of coupled heat and moisture transport in masonry, Computational homogenization with million-way parallelism using domain decomposition methods, Fully-coupled micro-macro finite element simulations of the Nakajima test using parallel computational homogenization, Sparse matrix factorization in the implicit finite element method on petascale architecture, Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections, A unified dual-primal finite element tearing and interconnecting approach for incompressible Stokes equations, Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics, A deluxe FETI-DP algorithm for a hybrid staggered discontinuous Galerkin method for H(curl)-elliptic problems, Classical and all-floating FETI methods for the simulation of arterial tissues, Bridging multiple structural scales with a generalized finite element method, Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models, A 3D domain decomposition approach for the identification of spatially varying elastic material parameters, Simultaneous FETI and block FETI: Robust domain decomposition with multiple search directions, A two‐level domain decomposition method with accurate interface conditions for the Helmholtz problem, A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices, Substructured formulations of nonlinear structure problems - influence of the interface condition, Integrated finite element neural network (I-FENN) for non-local continuum damage mechanics, Use of algebraic dual spaces in domain decomposition methods for Darcy flow in 3D domains, Adaptive and frugal FETI-DP for virtual elements, Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results, The impact of enabling multiple subdomains per MPI process in the TFETI domain decomposition method, Balancing domain decomposition method for large-scale analysis of an assembly structure having millions of multipoint constraints, BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields, FETI-DP for the Three Dimensional Virtual Element Method, Balancing Domain Decomposition by Constraints Algorithms for Curl-Conforming Spaces of Arbitrary Order, A Coarse Space to Remove the Logarithmic Dependency in Neumann–Neumann Methods, The HTFETI Method Variant Gluing Cluster Subdomains by Kernel Matrices Representing the Rigid Body Motions, Hybrid TFETI domain decomposition with the clusters joined by faces' rigid modes for solving huge 3D elastic problems, Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners, A Robust Preconditioner for High-Contrast Problems (Research), Nested BDDC for a saddle-point problem, High scalable non-overlapping domain decomposition method using a direct method for finite element analysis, Dual-primal domain decomposition method for uncertainty quantification, Robust Preconditioners via Generalized Eigenproblems for Hybrid Sparse Linear Solvers, A FETI-DP Formation for the Stokes Problem Without Primal Pressure Components, BDDC and FETI-DP Preconditioners for Spectral Element Discretizations of Almost Incompressible Elasticity, A domain decomposition strategy to efficiently solve structures containing repeated patterns, Convergence analysis of a balancing domain decomposition method for solving a class of indefinite linear systems, BDDC and FETI-DP under minimalist assumptions, A Rigorous Error Analysis of Coupled FEM-BEM Problems with Arbitrary Many Subdomains, FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING, The multipliers-free domain decomposition methods, On the Moore–Penrose inverse in solving saddle‐point systems with singular diagonal blocks, A scalable FETI-DP algorithm for a coercive variational inequality, Nonoverlapping discretization methods for partial differential equations, Non-overlapping domain decomposition method for a nodal finite element method, The three-field formulation for elasticity problems, FETI Domain Decomposition Methods for Second Order Elliptic Partial Differential Equations, FER/SubDomain: An Integrated Environment for Finite Element Analysis using Object-Oriented Approach, Low-Rank Approximation of Elliptic Boundary Value Problems with High-Contrast Coefficients, Domain decomposition approach to flexible multibody dynamics simulation, Machine Learning in Adaptive Domain Decomposition Methods---Predicting the Geometric Location of Constraints, Fast iterative solver for convection-diffusion systems with spectral elements, Combining Machine Learning and Adaptive Coarse Spaces---A Hybrid Approach for Robust FETI-DP Methods in Three Dimensions, Auxiliary Space Multigrid Method for Elliptic Problems with Highly Varying Coefficients, A Nonlinear FETI-DP Method with an Inexact Coarse Problem, BDDC Deluxe Domain Decomposition, A Newton-Krylov-FETI-DP Method with an Adaptive Coarse Space Applied to Elastoplasticity, Condition number bounds for IETI-DP methods that are explicit in h and p, Dual-Primal Isogeometric Tearing and Interconnecting Methods, Towards a multi‐scale computerized bone diagnostic system: 2D micro‐scale finite element analysis, Adaptive Coarse Spaces for FETI-DP in Three Dimensions, Multipliers-free dual-primal domain decomposition methods for nonsymmetric matrices and their numerical testing, The Schwarz alternating method in solid mechanics, Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption, Physics-based balancing domain decomposition by constraints for multi-material problems, A Padé-based factorization-free algorithm for identifying the eigenvalues missed by a generalized symmetric eigensolver, Multi-scale domain decomposition method for large-scale structural analysis with a zooming technique: Application to plate assembly, PCBDDC: A Class of Robust Dual-Primal Methods in PETSc, On adaptive BDDC for the flow in heterogeneous porous media., The all-floating boundary element tearing and interconnecting method, A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems, BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS, Scaling up through domain decomposition, Block FETI–DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity, Vertex-Based Preconditioners for the Coarse Problems of BDDC, Local Fourier Analysis of Balancing Domain Decomposition By Constraints Algorithms, BDDC domain decomposition algorithms, Total FETI-an easier implementable variant of the FETI method for numerical solution of elliptic PDE, Unnamed Item, Distributed algebraic tearing and interconnecting techniques, The mosaic of high-performance domain decomposition methods for structural mechanics. II: Formulation enhancements, multiple right-hand sides and implicit dynamics, A FETI-DP Type Domain Decomposition Algorithm for Three-Dimensional Incompressible Stokes Equations, Recent Advances in Domain Decomposition Methods for the Stokes Problem, A Parallel Crank–Nicolson Predictor-Corrector Method for Many Subdomains, Hybrid Dual-Primal FETI-Schur Complement Method for Stokes, The approximate component mode synthesis special finite element method in two dimensions: parallel implementation and numerical results
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems
- NURBS approximation of surface / surface intersection curves
- Extending substructure based iterative solvers to multiple load and repeated analyses
- Convergence of a substructuring method with Lagrange multipliers
- The two-level FETI method for static and dynamic plate problems I: An optimal iterative solver for biharmonic systems
- The two-level FETI method II: Extension to shell problems, parallel implementation and performance results
- On a component mode synthesis method and its application to incompatible substructures
- An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems
- A method of finite element tearing and interconnecting and its parallel solution algorithm
- A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers
- A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems
- A Scalable Substructuring Method by Lagrange Multipliers for Plate Bending Problems
- On the general solution by a direct method of a large-scale singular system of linear equations: application to the analysis of floating structures
- Application of the FETI method to ASCI problems?scalability results on 1000 processors and discussion of highly heterogeneous problems
- Mesh partitioning for implicit computations via iterative domain decomposition: Impact and optimization of the subdomain aspect ratio
- A scalable Lagrange multiplier based domain decomposition method for time‐dependent problems
- Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver