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Showing 1 to 20 of 52 for “"Preconditioners"”.
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Recycling Krylov Subspaces and Preconditioners
… algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual linear systems may …
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Preconditioners for Generalized Saddle -Point Problems
… illustrating the eigenvalue bounds on our preconditioners and demonstrating the theoretical justification of these methods. We also present convergence and timing results, showing the effectiveness of our methods in practice. Specifically the use of probing methods for approximating the …
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Spectral element poisson preconditioners for heterogeneous architectures
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms
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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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Reusing and Updating Preconditioners for Sequences of Matrices
… the benefits of both reusing and recycling preconditioners, with special focus on ILUTP and factorized sparse approximate inverses and proposes an update that we refer to as a sparse approximate map or SAM update. Analysis of the residual and eigenvalues of the map will be provided. …
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Domain decomposition preconditioners for higher-order discontinuous Galerkin discretizations
… reduced CPU time. The domain decomposition preconditioners are extended to solve the Euler and Navier- Stokes systems of equations. An analysis is performed to determine the effect of boundary conditions on the convergence of domain decomposition methods. Optimized Robin-Robin interface …
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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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Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem
When trying to solve elliptical problems such as the Poisson problem on complicated domains, one procedure is to split the domain into a union of simpler subdomains. When solving these problems iteratively, it becomes important to be able to precondition the coupling between the subdomains. Using …
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Preconditioning of Karush--Kuhn--Tucker Systems arising in Optimal Control Problems
This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush--Kuhn--Tucker (KKT) optimality conditions or in interior--point …
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Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations
… methods are considered. With overlapping DD preconditioners, we work on a time dependent CDR model. The additive Runge-Kutta (ARK) scheme is used for the time discretization and the fourth-order finite volume is applied for the spacial discretization. With the non-overlapping DD methods, some …
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Domain decomposition methods for time-harmonic elastic waves
… can be used as iterative solvers but also as preconditioners in a Krylov type method. That is the reason why transmission conditions between subdomains are very important.In this manuscript, we start by an overview of main domain decomposition methods and focus first on their use as …
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Low-order finite element preconditioner for spectral element pressure solver in Navier-Stokes equations
… be better than traditional schemes. With these preconditioners a bound on the number of iterations is attained regardless of mesh geometry or polynomial degree used. This novel meshing strategy achieves a reduction up to 30% in the number of iterations compared to the best current schemes …
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Preconditioning For Matrix Computation
… when we apply Gaussian random matrices as preconditioners. We confirm these results with our extensive numerical tests. The tests also show that the same methods work as efficiently on the average when we use random structured, in particular circulant, preconditioners instead, but we show …
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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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ILU and Machine Learning Based Preconditioning For The Discretized Incompressible Navier-Stokes Equations.
… Navier-Stokes equations. The corresponding preconditioners are used to accelerate the convergence of the GMRES method. Stabilized and unstabilized nite element methods are used for the Navier-Stokes problem leading to systems of algebraic equations of a saddle point type, which has a 2 …
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Some new results for solving linear systems arising from computational fluid dynamics problems
… definite systems, we propose a class of nested preconditioners and analyze properties of these preconditioners. Some necessary and sufficient conditions for the optimality of these nested preconditioners are established. Finally, for unsymmetric systems, we generalize the concept of spectral …
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Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems
… iterative methods and, in particular, efficient preconditioners need to be developed. In this study, we consider application of incomplete LU (ILU) preconditioners for finite element models to partial differential equations. Since finite elements lead to large, sparse systems, reordering the node …
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Innovative Methods for Solving Multicomponent Biogeochemical Groundwater Transport on Supercomputers
… performed superior to conventional preconditioners (i.e. faster simulation time and better parallel scalability) for scenarios exhibiting little solute retardation. However, Matrix-Lite preconditioning was required for scenarios with severely retarded reaction fronts. Although this …
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Parallel Black Oil Solvers on GPU
… package, several different linear solvers and preconditioners have been implemented based on GPU. For solvers, it has GMRES, BICGSTAB, ORTHOMIN etc, which are commonly used in reservoir simulators. For preconditioners, a group of ILU preconditioners are developed on GPU, including ILU(0), ILUT, …
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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… method employed in a Hessian-free manner. The preconditioners have an inner-outer structure, taking the form of a Schur complement (block factorization) at the outer level and Schwarz projections at the inner level. However, building an exact Schur complement is prohibitively expensive. Thus, …
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