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Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear PoissonBoltzmann Equation
, 1107
"... In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such as the nonlinear PoissonBoltzmann equation and its regular ..."
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Cited by 2 (1 self)
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In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such as the nonlinear PoissonBoltzmann equation and its
Iterative Solution of Elliptic Finite Element Problems on Partially Refined Meshes and the Effect of Using Inexact Solvers
, 1993
"... We will consider some solution methods for the linear systems of algebraic equations which arise from secondorder elliptic finite element problems. We first consider iterative refinement methods. Historically these methods were called FAC and AFAC methods. Optimal bounds of the condition number for ..."
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Cited by 8 (1 self)
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general assumption. The optimality of the FAC method when spectrally equivalent inexact solvers are used is also proved by using similar techniques. We next consider multilevel additive Schwarz methods with partial refinement. These algorithms are generalizations of the multilevel additive Schwarz methods
The Domain Reduction Method: High Way Reduction In Three Dimensions And Convergence With Inexact Solvers
 in Fourth Copper Mountain conference on multigrid methods
, 1989
"... . We study a method for parallel solution of elliptic partial differential equations which decomposes the problem into a number of independent subproblems on subspaces of the underlying solution space. Using symmetries of the domain, we obtain up to 64 such subproblems for a 3 dimensional cube and t ..."
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Cited by 9 (7 self)
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and the method reduces to a direct solver. In the general case, or when the subproblems are solved only approximately, the method becomes an iterative method or can be used as a preconditioner. Bounds on the resulting convergence factors and condition numbers are given. 1. Introduction. In this paper, we
BDDC Preconditioning for HighOrder Galerkin Least Squares Methods using Inexact Solvers
, 2009
"... A highorder Galerkin LeastSquares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for largescale, convectiondominated problems. The algorithm is applied ..."
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Cited by 1 (1 self)
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A highorder Galerkin LeastSquares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for largescale, convectiondominated problems. The algorithm
Inexact Solvers for Saddlepoint System Arising from Domain Decomposition of Linear Elasticity Problems in Three Dimensions
"... In this paper, a domain decomposition method with lagrange multipliers based on geometrically nonconforming subdomain partitions for three dimensional linear elasticity is considered. Because of the geometrically nonconforming partitions, appropriate multiplier spaces should be chosen, and a sadd ..."
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saddlepoint system is then built. An augmented technique is introduced, such that the resulting new saddlepoint system can be solved by the existing iterative methods. Two simple inexact preconditioners are constructed for the saddlepoint system, one for the displacement variable, and the other
THE DOMAIN REDUCTION METHOD: HIGH WAY REDUCTION IN THREE DIMENSIONS AND CONVERGENCE WITH INEXACT SOLVERS
"... Abstract. We study a method for parallel solution of elliptic partial di erential equations which decomposes the problem into a number of independent subproblems on subspaces of the underlying solution space. Using symmetries of the domain, we obtain up to 64 such subproblems for a 3 dimensional cub ..."
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cube and the method reduces to a direct solver. In the general case, or when the subproblems are solved only approximately, the method becomes an iterative method or can be used as a preconditioner. Bounds on the resulting convergence factors and condition numbers are given.
Solvers by Inexact Subsystem Simulations
"... This paper is concerned with the numerical solution of systems of blocked nonlinear equations arising in the solution of Multidisciplinary Analysis (MDA) problems. We consider the case where individual discipline solvers/simulators are given and are iterative methods. Thus, an MDA solver consists of ..."
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This paper is concerned with the numerical solution of systems of blocked nonlinear equations arising in the solution of Multidisciplinary Analysis (MDA) problems. We consider the case where individual discipline solvers/simulators are given and are iterative methods. Thus, an MDA solver consists
Globalization strategies for inexactNewton solvers
, 2009
"... Globalization strategies are necessary in practical inexactNewton flow solvers to ensure convergence when the initial iterate is far from the solution. In this work, we present two novel globalizations based on parameter continuation. The first continuation method parameterizes the boundary conditi ..."
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Globalization strategies are necessary in practical inexactNewton flow solvers to ensure convergence when the initial iterate is far from the solution. In this work, we present two novel globalizations based on parameter continuation. The first continuation method parameterizes the boundary
Inexact Inverse Iteration for Symmetric Matrices
"... In this paper we analyse inexact inverse iteration for the real symmetric eigenvalue problem Av = v. Our analysis is designed to apply to the case when A is large and sparse and where iterative methods are used to solve the shifted linear systems (A I)y = x which arise. We present a convergence th ..."
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theory that is independent of the nature of the inexact solver used, and, though the use of the Rayleigh quotient is emphasised, our analysis also extends to quite general choices for shift and inexact solver strategies. Additionally, the convergence framework allows us to treat both standard
Acceleration of Multidisciplinary Analysis Solvers by Inexact Subsystem Simulations
, 1998
"... This paper is concerned with the numerical solution of systems of blocked nonlinear equations arising in the solution of Multidisciplinary Analysis (MDA) problems. We consider the case where individual discipline solvers/simulators are given and are iterative methods. Thus, an MDA solver consists of ..."
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Cited by 1 (0 self)
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This paper is concerned with the numerical solution of systems of blocked nonlinear equations arising in the solution of Multidisciplinary Analysis (MDA) problems. We consider the case where individual discipline solvers/simulators are given and are iterative methods. Thus, an MDA solver consists
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