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Showing 1 to 20 of 74 for “"preconditioner"”.
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An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations
… research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability …
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Polynomial reduction with full domain decomposition preconditioner for spectral element poisson solvers
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-04-12 without embargo terms
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Spectral Model Reduction as Preconditioner and Adaptive Solver Component in Chemical Reaction Systems
Die vorliegende Arbeit besch\"aftigt sich mit der Analyse und der Anwendung der Reduktionsmechanismen QSSA und ILDM, die beide im Rahmen der Modellierung von chemischen Verbrennungsprozessen entwickelt worden sind. Beide Mechanismen reduzieren die Anzahl der zu modellierenden Spezies erheblich, was …
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Low-order finite element preconditioner for spectral element pressure solver in Navier-Stokes equations
… points in the SEM discretization is proposed as preconditioner. Three different versions of the preconditioner based on combinations of the low-order stiffness and mass matrices are tested for 2D and 3D geometries. When building the preconditioning operators a new meshing approach that allows …
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A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization
… on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(O)) is also presented as a preconditioner, where the factorization is performed using a …
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Domain decomposition preconditioners for higher-order discontinuous Galerkin discretizations
… A minimum overlapping additive Schwarz (ASM) preconditioner and a Balancing Domain Decomposition by Constraints (BDDC) preconditioner are developed for the HDG discretization. An algebraic coarse space for the ASM preconditioner is developed based on the solution of local harmonic problems. …
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Domain Decomposition Preconditioners for Hermite Collocation Problems
… of Krylov subspace methods with parallelizable preconditioners is essential for obtaining effective iterative solvers for very large linear systems of equations. Substructuring provides a framework for constructing robust and parallel preconditioners for linear systems arising from the …
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3-D Modeling of Ductile Tearing Using Finite Elements: Computational Aspects and Techniques
… of the Hughes-Winget element-by-element (HW) preconditioner. The implementation employs a weighted dependency graph combined with a new coloring algorithm to provide load-balanced scheduling for the preconditioner and overlapped communication/computation. This approach enables efficient …
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Reusing and Updating Preconditioners for Sequences of Matrices
… of related linear systems, the computation of a preconditioner for every system can be expensive. Often a fixed preconditioner is used, but this may not be effective as the matrix changes. This research examines the benefits of both reusing and recycling preconditioners, with special focus on …
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Recycling Techniques for Sequences of Linear Systems and Eigenproblems
… Recycling techniques, such as recycling preconditioners or subspaces, are popular approaches for reducing computational cost. In this thesis, we introduce two novel approaches for recycling previously computed information for a subsequent system or eigenproblem, and demonstrate good …
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Recycling Preconditioners for Sequences of Linear Systems and Matrix Reordering
… subspace methods and how to obtain effective preconditioners inexpensively. We first present an application for electronic structure calculation. A sequence of slowly changing linear systems is produced in the simulation. The linear systems change by rank-one updates. Properties of the system …
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Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems
… methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method …
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Fast Solvers for Models of Fluid Flow with Spectral Elements
… solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the "least-squares commutator" preconditioner, originally …
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Incomplete factorization preconditioning for linear least squares problems
A new family of preconditioners for conjugate gradient-like iterative methods applied to large sparse linear least squares problems, $min\Vert Ax-b\Vert\sb2$, is proposed. The family is based on incomplete Gram-Schmidt (IGS) factorizations of A. Particular attention has been given to the following …
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GPU-accelerated Linear Solvers for High-order Finite Element Methods in Poisson Problems
… rate enhanced through the application of a preconditioner. Novel smoothers are constructed within a multigrid preconditioner to improve the convergence rate on highly deformed meshes. Additionally, new stopping criteria are introduced to balance various error sources, thereby reducing the …
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A family of preconditioned iterative solvers for sparse linear systems
… robustness by reevaluating a parametrized preconditioner whenever poor convergence or instability is encountered. We present numerical experiments that demonstrate the efficiency of several members of this new family in comparison with other known methods, in the context of PARASPAR, and in …
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A Nodal Approach to Arbitrary Geometries, and Adaptive Mesh Refinement for the Nodal Method
… of the NIM to incorporate fast and accurate preconditioner and solver routines. Application of this modified implementation to convection-diffusion problems proves that the coarse mesh efficiency of the nodal method can be maintained by taking advantage of ""off the shelf"" advanced solver …
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The solution of large viscoelastic flow problems using parallel iterative techniques
… using an algorithm which combines a parallel preconditioner with a Krylov subspace method. The parallel preconditioner, called the Block Complement and Additive Levels Method (BCALM) preconditioner, is based on treating pressure unknowns separately from the variables velocities and gradients. …
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Parallel Domain Decomposition Preconditioning for the Adaptive Finite Element Solution of Elliptic Problems in Three Dimensions
… of overlap is sufficient to yield an optimal preconditioner. The number of elements in this overlap region between subdomains is O(h-2 ) as the mesh size h -> 0. This is an improvement over the O(h-3) overlapping elements required to obtain optimality for a conventional two level additive …
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Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem
… that this procedure does create an efficient preconditioner to get at the coupling between subdomains.
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