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Adaptive Three-Level BDDC Using Frugal Constraints
The convergence rate of both the FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal) and the BDDC (Balancing Domain Decomposition by...
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Reynolds-BlendedWeights for BDDC in Applications to Incompressible Flows
We investigate the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to numerical solution of problems of...
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Three-Level BDDC for Virtual Elements
The Virtual Element Method (VEM) is a Galerkin-type method for the solution of partial differential equations which allows for the discretization...
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BDDC Preconditioners for Divergence Free Virtual Element Discretizations of the Stokes Equations
The virtual element method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of...
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Newton–Krylov-BDDC deluxe solvers for non-symmetric fully implicit time discretizations of the bidomain model
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac...
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Application of Multilevel BDDC to the Problem of Pressure in Simulations of Incompressible Flow
We deal with the numerical solution of problems of incompressible flows and investigate the applicability of the Balancing Domain Decomposition by...
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Adaptive BDDC Based on Local Eigenproblems
FETI-DP (dual-primal finite element tearing and interconnecting) and BDDC (balancing domain decomposition by constraints) are among the leading...
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Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions
Adaptive, that is, problem-dependent coarse spaces provide a robust condition number estimate and thus a robust convergence behavior for FETI-DP...
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BDDC for a Saddle Point Problem with an HDG Discretization
The Balancing Domain Decomposition by Constraints (BDDC) algorithms, introduced in [4], are nonoverlap** domain decomposition methods. The coarse...
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On Inexact Solvers for the Coarse Problem of BDDC
In this study, we present Balancing Domain Decomposition by Constraints (BDDC) preconditioners for three-dimensional scalar elliptic and linear...
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On adaptive BDDC for the flow in heterogeneous porous media
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for numerical solution of a single-phase flow in heterogeneous porous...
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Dual-Primal Preconditioners for Newton–Krylov Solvers for the Cardiac Bidomain Model
We present here an overview of Newton–Krylov solvers for implicit time discretizations of the cardiac Bidomain equations, preconditioned by Balancing...
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Robust Model Reduction Discretizations Based on Adaptive BDDC Techniques
Recently, methods that do not rely on the regularity of the solution were introduced: generalized finite element methods [1], the rough polyharmonic...
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BDDC Preconditioners for a Space-time Finite Element Discretization of Parabolic Problems
Continuous space-time finite element methods for parabolic problems have been recently studied, e.g., in [1, 9, 10, 13]. The main common features of...
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A Closer Look at Local Eigenvalue Solvers for Adaptive FETI-DP and BDDC
In order to obtain a scalable domain decomposition method (DDM) for elliptic problems, a coarse space is necessary and an associated coarse problem...
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Scalable and Robust Dual-Primal Newton–Krylov Deluxe Solvers for Cardiac Electrophysiology with Biophysical Ionic Models
The focus of this work is to provide an extensive numerical study of the parallel efficiency and robustness of a staggered dual-primal Newton–Krylov...
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Adaptive Schwarz Method for a Non-Conforming Crouzeix-Raviart Discretization of a Multiscale Elliptic Problem
In many physical or engineering practical applications, we see a heterogeneity of coefficients; e.g., in ground flow problems in heterogeneous media.
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Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces
Nonlinear domain decomposition methods (DDMs) are based on a decomposition of a discretized nonlinear partial differential equation instead of...
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On Global and Monotone Convergence of the Preconditioned Newton’s Method for Some Mildly Nonlinear Systems
Let β be a diagonal map** from RN to itself and let A be an N X N real matrix.
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Composing Two Different Nonlinear FETI–DP Methods
Nonlinear FETI–DP methods [3] are nonlinear generalizations of linear FETI–DP domain decomposition methods [10].