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Showing 1 to 20 of 44 for “"GMRES"”.
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Parallel Sparse Linear Algebra for Homotopy Methods
… research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strategy of GMRES(k) allows tuning of the restart parameter k based on the GMRES convergence rate for the given problem. Adaptive GMRES(k) is shown to be superior …
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Analysis and Implementation Considerations of Krylov Subspace Methods on Modern Heterogeneous Computing Architectures
… Thefirst analyzes the performance of block GMRES (BGMRES) compared to GMRES for linear systems with multiple right hand sides (RHS) on both CPUs and GPUs, and modelling when BGMRES is most advantageous over GMRES on the GPU. On CPUs, the current paradigm is that if one wishes to solve a …
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A family of preconditioned iterative solvers for sparse linear systems
… which comprise the Broyden methods, GCR, GMRES, Newton's method for approximating the inverse, and a combination of a Galerkin step followed by a step of Richardson's method. Scaling-invariant versions and implementations of higher efficiency are developed, and their complexity is …
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Hamiltonian Paths and Strands for Unified Grid Approach for Computing Aerodynamic Flows
… further using Generalized Minimum Residual (GMRES) method. GMRES requires a preconditioning step which is performed using the line-implicit method. GMRES provides better convergence rate than the pure line-implicit method at various flow conditions. Both parts of mesh generation and flow …
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ILU and Machine Learning Based Preconditioning For The Discretized Incompressible Navier-Stokes Equations.
… iterative Krylov-subspace methods, such as GMRES, to solve large and sparse linear algebraic systems that result from a Galerkin nite element (FE) discretizations of the linearized Navier-Stokes equations. The corresponding preconditioners are used to accelerate the convergence of the GMRES …
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Thomas Fermi model for mesons and new noise subtraction techniques in lattice QCD.
… This is done with linear equation solvers like GMRES-DR (Generalized Minimum RESidual algorithm-Deated and Restarted) for the first noise, and GMRES-Proj (similar algorithm projected over eigenvectors) for remaining noises. In this context, we are attempting to employ matrix deflation algorithms …
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Acceleration Techniques for Industrial Large Eddy Simulation with High-Order Methods on CPU-GPU Clusters
… methods are implemented on GPUs: the matrix-free GMRES solver and a novel local GMRES-SGS method. Parametric studies are done to evaluate their performance on LES benchmark cases. On the High-Lift Common Research Model case for the 2021 4th AIAA High-Lift Prediction Workshop, both GPU implicit …
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Performance of Algebraic Multigrid for Parallelized Finite Element DNS/LES Solvers
… AMG, and single-level ILUT preconditioned GMRES; and on two supercomputers of different memory architecture(distributed and shared memory). This study revealed Fourier space partitioning outperforms physical space partitioning in all problems analyzed, and scales more efficiently as well. …
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Numerical schemes and well-posedness in nonlinear aeroelasticity
… A solution strategy employing a Newton-GMRes algorithm is compared with coupling strategies that are usually employed in aeroelasticity.
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Thomas-Fermi quark model and techniques to improve lattice QCD calculation.
… one, which we call Polynomial-Preconditioned GMRES-DR(PP-GMRESDR), is used to speed up the calculation of large systems of linear equations in LQCD. The second one, called the Polynomial-Subtraction method, is used to help reduce the noise variance of the calculations for disconnected loops in …
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Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems
… problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse …
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Efficient Numeric Computation of a Phase Diagram in Biased Diffusion of Two Species
… The Crank-Nicholson, nonlinear Gauss-Seidel, and GMRES algorithms used to solve the model equations are discussed. Performance enhancements and limits on convergence are considered.
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Immersed Interface Method for Elasticity Problems with Interfaces
… The bi-conjugate gradient method and the GMRES with preconditioning are both implemented to solve the resulting linear systems of equations and compared. The level set method is used to represent the interface. Numerical results are presented to show that the immersed interface method is …
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ADMM Based Methods for Time-Domain Decomposition Formulations of Optimal Control Problems
… effectiveness of ADMM as a preconditioner within GMRES is investigated. Computational results are presented for several variants of ADMM applied to an advection-diffusion problem.
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A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization
… smoothing is presented as a preconditioner to GMRES.
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On the Use of Arnoldi and Golub-Kahan Bases to Solve Nonsymmetric Ill-Posed Inverse Problems
… is fundamental to the popular iterative method GMRES) has been of renewed interest recently. We discuss some of the positive and negative aspects of each process and use example problems to examine some qualities of the bases they produce. Computing optimal solutions in a given basis gives some …
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Brownian dynamics simulation of soft matter with hydrodynamics: methods for constrained systems and shear processing of 2D materials
… state-of-the-art method for these simulations, GMRES, to a different method called the projected conjugate gradient (PrCG) method. In particular, we compared PrCG and GMRES for rigid bodies, freely jointed chains, and immobile systems. We find that both methods exhibit the same linear …
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Exploiting compression in solving discretized linear systems
… elimination and iterative methods such as GMRES. This thesis proposes a method for exploiting compression while computing the solution to a given discretized system of linear algebraic equations and investigates both its overall effectiveness in practice and which factors determine its …
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FastStokes : a fast 3-D fluid simulation program for micro-electro-mechanical systems
… algorithm in combination with the GMRES algorithm substantially improves the speed of this simulation program. An efficient two-step approach that successfully handles the null space of the singular incompressible Stokes BEM operators is developed to avoid numerical errors and …
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High-order implicit large-eddy simulation for transitional aerodynamics flows
… equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The combination of hybridized DG methods with an efficient solution procedure leads to a high-order accurate NS solver that is competitive to alternative approaches, such as finite volume …
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