Electrostatic interactions between dielectric objects are complex and of a many-body nature, owing to induced surface bound charge. We present a collection of techniques to simulate dynamical dielectric objects. We calculate the surface bound charge from a matrix equation using the Generalized Minimal Residue method (GMRES). Empirically, we find that GMRES converges very quickly. Indeed, our de...

Low complexity equalization with LSRQ and GMRES algorithm is compared with traditional equalization methods. As the next generation technologies like LTE and WiMax have a large number of subcarriers the traditional equalization methods like MF, ZF, MMSE, VBLAST, and SAGE which require matrix inversion become highly complex in time and consume a lot of time to equalize the received signal. An al...

For quite some times, deflation preconditioner has been proposed and used to accelerate the convergence of Krylov subspace methods. For symmetric positive definite linear systems, convergence of CG combined with deflation has been analyzed and compared with other preconditioners, e.g. with the abstract balancing preconditioner [Nabben and Vuik, SIAM J. Sci. Comput., 27 (2006), pp. 1742–1759]. I...

The recently proposed method IDR(s) [6] for solving large and sparse nonsymmetric systems of linear equations has proven to be highly efficient for important classes of applications. This paper presents an performance comparison of IDR(s) with GMRES [3], Bi-CGSTAB [7] and BiCGstab(l) [4] for representative fluid dynamics test problems. The computations are done with the MATLAB finite element pr...

for x, where A is a given n × n matrix, and b a given n-vector. We have many opportunities to solve linear equations with the same coefficient matrix and different right-hand sides (RHSs). Therefore, block Krylov subspace methods such as the block Bi-CG (Bl-BCG), block Bi-CGSTAB (Bl-BiCGSTAB) [2], block GMRES (Bl-GMRES) and block QMR (Bl-QMR) methods have been developed for solving block linear...

Block-GMRES is an iterative method for solving nonsymmetric systems of linear equations with multiple right-hand sides. Restarting may be needed, due to orthogonalization expense or limited storage. We discuss how restarting affects convergence and the role small eigenvalues play. Then a version of restarted block-GMRES that deflates eigenvalues is presented. It is demonstrated that deflation c...