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Generalized Minimal Residual (generalized + minimal_residual)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

A 3-D non-hydrostatic pressure model for small amplitude free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006
J. W. Lee
Abstract A three-dimensional, non-hydrostatic pressure, numerical model with k,, equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure,Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement. Copyright © 2005 John Wiley & Sons, Ltd. [source]

SSOR preconditioned GMRES for the FEM analysis of waveguide discontinuities with anisotropic dielectric

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 2 2004
R. S. Chen
Abstract The anisotropic media and active properties of the perfectly matched layer (PML) absorbers significantly deteriorate the finite element method (FEM) system condition and as a result, convergence of the iterative solver is substantially slowed down. To address this issue, the symmetric successive over-relaxation (SSOR) preconditioning scheme is applied to the generalized minimal residual (GMRES) for solving a large sparse and non-symmetric system of linear equations resulting from the analysis of ferrite waveguide device by use of edge-based FEM. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES for the typical structures. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Application of the preconditioned GMRES to the Crank-Nicolson finite-difference time-domain algorithm for 3D full-wave analysis of planar circuits

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2008
Y. Yang
Abstract The increase of the time step size significantly deteriorates the property of the coefficient matrix generated from the Crank-Nicolson finite-difference time-domain (CN-FDTD) method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. To address this issue, this article mainly concerns efficient computation of this large sparse linear equations using preconditioned generalized minimal residual (PGMRES) method. Some typical preconditioning techniques, such as the Jacobi preconditioner, the sparse approximate inverse (SAI) preconditioner, and the symmetric successive over-relaxation (SSOR) preconditioner, are introduced to accelerate the convergence of the GMRES iterative method. Numerical simulation shows that the SSOR preconditioned GMRES method can reach convergence five times faster than GMRES for some typical structures. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1458,1463, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23396 [source]

Robust GMRES recursive method for fast finite element analysis of 3D electromagnetic problems

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2007
P. L. Rui
Abstract A robust generalized minimal residual recursive (GMRESR) iterative method is proposed to solve a large system of linear equations resulting from the use of an un-gauged vector-potential formulation of finite element method (FEM). This method involves an outer generalized conjugate residual (GCR) method and an inner generalized minimal residual (GMRES) method, where the inner GMRES acts as a variable preconditioning for the outer GCR. The efficient implementation of symmetric successive overrelaxation (SSOR) preconditioned GMRESR (SSOR-GMRESR) algorithm is described in details for complex coefficient matrix equation. On several three-dimensional electromagnetic problems, the resulting SSOR-GMRESR approach converges in CPU time, which is 14.2,71.3 times shorter with respect to conventional conjugate gradient (CG) approach. By comparison with other popularly preconditioned CG methods, the results demonstrate that SSOR-GMRESR is especially effective and robust when the A-V formulation of FEM is applied to solve large-scale time harmonic electromagnetic field problems. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1010,1015, 2007; Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.22333 [source]

BCCB preconditioners for systems of BVM-based numerical integrators

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2004
Siu-Long Lei
Abstract Boundary value methods (BVMs) for ordinary differential equations require the solution of non-symmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditioner is shown to be invertible when the BVM is Ak1,k2 -stable. The spectrum of the preconditioned matrix is clustered and therefore, the preconditioned GMRES method converges fast. Moreover, the operation cost in each iteration of the preconditioned GMRES method by using our BCCB preconditioner is less than that required by using block-circulant preconditioners proposed earlier. In numerical experiments, we compare the number of iterations of various preconditioners. Copyright © 2003 John Wiley & Sons, Ltd. [source]