Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results
From MaRDI portal
Publication:4594170
DOI10.1137/16M1102495zbMath1377.65163OpenAlexW2770488629MaRDI QIDQ4594170
Oliver Rheinbach, Matthias Uran, Axel Klawonn, Martin Lanser
Publication date: 17 November 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/16m1102495
Newton's methodNewton-Krylov methodsparallel computingpreconditionernonlinear problemsbalancing domain decomposition by constraintnonlinear eliminationnonlinear domain decompositionfinite element tearing and interconnecting -- dual-primal
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Nonlinear elliptic equations (35J60) Parallel numerical computation (65Y05) Preconditioners for iterative methods (65F08)
Related Items (16)
Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner ⋮ Linear and nonlinear substructured restricted additive Schwarz iterations and preconditioning ⋮ A Nonlinear Elimination Preconditioned Inexact Newton Algorithm ⋮ 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 ⋮ Adaptive Nonlinear Domain Decomposition Methods with an Application to the $p$-Laplacian ⋮ On the Accuracy of the Inner Newton Iteration in Nonlinear Domain Decomposition ⋮ Nonlinear BDDC methods with approximate solvers ⋮ Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids ⋮ A frugal FETI-DP and BDDC coarse space for heterogeneous problems ⋮ Machine Learning in Adaptive Domain Decomposition Methods---Predicting the Geometric Location of Constraints ⋮ Preconditioning the coarse problem of BDDC methods ‐ three-level, algebraic multigrid, and vertex-based preconditioners ⋮ A Nonlinear Elimination Preconditioned Inexact Newton Method for Heterogeneous Hyperelasticity ⋮ 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 ⋮ On the performance of domain decomposition methods for modeling heterogenous materials
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An algebraic theory for primal and dual substructuring methods by constraints
- Robust FETI-DP methods for heterogeneous three dimensional elasticity problems
- A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms
- \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
- Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
- FETI-DP: a dual-primal unified FETI method?part I: A faster alternative to the two-level FETI method
- Composing Scalable Nonlinear Algebraic Solvers
- A Nonlinear FETI-DP Method with an Inexact Coarse Problem
- Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method
- Nonlinear FETI-DP and BDDC Methods
- Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity
- On an Adaptive Coarse Space and on Nonlinear Domain Decomposition
- A Highly Scalable Implementation of Inexact Nonlinear FETI-DP Without Sparse Direct Solvers
- Nonlinear Overlapping Domain Decomposition Methods
- Dual-primal FETI methods for linear elasticity
- FETI-DP, BDDC, and block Cholesky methods
- Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations
- Multilevel Balancing Domain Decomposition at Extreme Scales
- Inexact FETI-DP methods
- A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
- Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
- A Preconditioner for Substructuring Based on Constrained Energy Minimization
- Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients
- Nonlinearly Preconditioned Inexact Newton Algorithms
- Non‐linear additive Schwarz preconditioners and application in computational fluid dynamics
- Choosing the Forcing Terms in an Inexact Newton Method
- An Analysis of Approximate Nonlinear Elimination
- Iterative Solution of Nonlinear Equations in Several Variables
- Field-Split Preconditioned Inexact Newton Algorithms
- New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables
- Convergence of a balancing domain decomposition by constraints and energy minimization
- A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
- Highly scalable parallel domain decomposition methods with an application to biomechanics
This page was built for publication: Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results
