Krylov subspace
Krylov Subspace Solvers and Preconditioners
... methods. Krylov subspace methods and multigrid are discussed in Saad [38] and Trottenberg, Oosterlee and Sch¨ uller ...on Krylov subspace methods are [1, 6, 21, 34, ...
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Parallel Implementation of Hybrid Direct-Iterative Algorithm for Multibody Dynamics via Krylov Subspace Methods on IBM 1350 Cluster
... Figure 6: Time Histories of Generalized Coordinates Table 2 shows average time cost of a function evaluation of six cases with application of five Krylov subspace methods in Aztec to each case. Take case 4 ...
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Krylov Subspace Spectral Methods for the Time-Dependent Schr¨odinger Equation with Non-Smooth Potentials
... other Krylov subspace methods (see, for example, [10]) for stiff systems of ODE, and, as shown in [11], they are also quite stable, considering that they are explicit ...
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Krylov subspace time domain computations of monochromatic sources for multi frequency optical response
... In Krylov subspace expo- nential time integration methods the system is projected on a smaller system of ODEs, this projection is made independent of the temporal part of the ...
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Comparison of Fixed Point Methods and Krylov Subspace Methods Solving Convection Diffusion Equations
... The paper first introduces two-dimensional convection-diffusion equation with boundary value condition, later uses the finite difference method to discretize the equation and analyzes positive definite, diagonally ...
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A Multigrid Block Krylov Subspace Spectral Method for Variable-Coefficient Elliptic PDE
... Abstract—Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solv- ing time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for ...
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Krylov subspace methods for time modeling of photonic crystals
... and Krylov simulations of a few different scenarios and for a number of grid ...that Krylov subspace methods are way more efficient than FDTD if a high accuracy is ...integration. Krylov ...
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Reduced Rank Adaptive Filtering Using Krylov Subspace
... on Krylov subspace is pre- sented and their interrelationship is ...discussed. Krylov sub- space methods are widely used in computational linear al- gebra for solving large (possibly sparse) systems ...
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Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE
... In [12] a class of methods, called Krylov subspace spectral (KSS) methods, was introduced for the purpose of solv- ing parabolic variable-coefficient PDE. These methods are based on techniques developed by ...
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Analysis of a Krylov subspace enhanced parareal algorithm for linear problems
... We start by considering the homogeneous case; we will see later that the inhomogeneous case can also be treated in a similar manner. In the correction step (2.3) of the original parareal algorithm, the fine propagator is ...
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Solution of Time-Dependent PDE Through Component-wise Approximation of Matrix Functions
... other Krylov subspace methods (see, for example, [14]) for stiff systems of ODE, and they are also quite stable, considering that they are explicit ...
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SVD MPE: An SVD Based Vector Extrapolation Method of Polynomial Type
... In this work, we develop yet another polynomial type method, which is based on the singular value decompo- sition (SVD), as well as some ideas that lead to MPE. We denote this new method by SVD-MPE. We also de- sign a ...
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Numerical Verification of 10000-dimensional Linear Systems 10000x Faster
... Tool Presentation: We evaluate an improved reachability algorithm for linear (and affine) systems implemented in the continuous branch of the Hylaa tool. While Hylaa’s earlier approach required n simulations to verify an ...
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Preconditioners based on splitting for time domain photonic crystal modeling
... Today the Maxwell equations of electrodynamics are still solved using the finite-difference time-domain method, because of the relative simplicity of the method. In order to solve these equations on an infinite domain, ...
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Krylov deferred correction methods for differential equations with algebraic constraints
... “averaged” constant coefficient elliptic equation, and the procedure is performed in the frequency domain. Analytical results show that the new equation system is Fredholm second kind (as the Green’s function captures ...
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An Explicit, Stable, High-Order Spectral Method for the Wave Equation Based on Block Gaussian Quadrature
... of Krylov Subspace Spectral (KSS) Methods, which build on the work of Golub, Meurant and others per- taining to moments and Gaussian quadrature to pro- duce high-order accurate approximate solutions to the ...
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Improved Krylov-FSP Method for Solving the Chemical Master Equation
... adaptive Krylov-FSP [2] that was driven by the stochastic simulation algorithm ...variable Krylov subspace dimension and a refined strategy for monitoring the ...
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An Improved Wavelet Based Preconditioner for Sparse Linear Problems
... for Krylov subspace iterative methods for ill conditioned sparse matrices and shown that these preconditioners are more effective compared with that of classical preconditioners by ap- plying them to ...
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A survey of methods for computing large sparse matrix exponentials arising in Markov modelling
... Krylov subspace techniques have been shown to yield robust methods for the nu- merical computation of large sparse matrix exponentials and especially the transient solutions of Markov ...a ...
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Magnetohydrodynamic modeling of solar magnetic arcades using exponential propagation methods
... the Krylov subspace approximation to the functions of matrices and showed how these concepts can be used to construct an ecient numerical technique for time integration of large s- ti systems of dierential ...
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