GMRESGeneralized Minimal Residual Algorithm
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SADOK, Global FOM and GMRES algorithms for matrix equations, Appl.
Central to the usual implementations of block GMRES is the block Arnoldi process [1], which can be used to construct the orthonormal basis of [K.sub.m](A, [R.sub.0]).
The surface current distribution computed by the H-LU preconditioned GMRES solver with [10.sup.-4] relative residual is also presented in Fig.
Linear system (111) is solved in O(n ln n) operations by the fast method presented in [11, 12] which is based on a combination of the MATLAB function gmres and the MATLAB function zfmm2dpart in the MATLAB toolbox FMMLIB2D [13].
CPU time analysis--[n.sub.f]--number of frequency samples, [n.sub.[theta]]--number of angle source samples, [t.sub.q]] = CPU time in seconds to generate moments, [t.sub.z] = CPU time in seconds to generate the coupling matrix derivatives, [t.sub.b] = CPU time in seconds to generate the incident vector derivatives, [t.sub.s] = average CPU time in seconds to solve for RCS at each frequency using a GMRES with tolerance [10.sup.-6], [t.sub.t] = total CPU time in seconds to generate and solve case study problem.
In the present work, the system of equations is solved using generalized minimal residual (GMRES) method [18].
Most of the research on iterative methods deals with iterative methods for solving linear systems of equalities and inequalities for sparse matrices, the most important method being GMRES method.
The chosen solver has been the Generalized Minimal RESidual algorithm for solving nonsymmetric linear systems, GMRES (Saad and Schultz 1986); the preconditioner used in the simulations was the Geometric Multigrid one, which allows it to accelerate the convergence of the base iterative method by correcting, from time to time, the solution globally by solving a coarse problem.
THIF-23: GMRES Preconditioners for Multivariate Steady-state Time-domain Method