Non-linear Eq.s occur as a sub-problem in wide variety of engineering and scientific domains. To deal with the complexity Eq.s, it is often required to use numerical procedures, which are most suitable method employ certain circumstances. Many classic iterative approaches have been regularly employed for various situations; nevertheless, convergence rate those methods low. In many cases, an app...

The subject of this paper is the comparison of Direct and Iterative solvers in the Solution of large Finite Element Problems with MSC/NASTRAN. The results of such a comparison vary based on problem type and with new developments in both the direct and iterative solution techniques. This paper gives the current state of this comparison with MSC/NASTRAN V70.5. Experiences gained in the past show ...

Direct methods for solving sparse systems of linear equations are fast and robust, but can consume an impractical amount of memory, particularly for large three-dimensional problems. Preconditioned iterative solvers have the potential to solve very large systems with a fraction of the memory used by direct methods. The diversity of preconditioners makes it difficult to analyze them in a unified...

The gap between the cost of moving data and the cost of computing continues to grow, making it ever harder to design iterative solvers on extreme-scale architectures. This problem can be alleviated by alternative algorithms that reduce the amount of data movement. We investigate this in the context of Lattice Quantum Chromodynamics and implement such an alternative solver algorithm, based on do...

The numerical solution of partial differential equations frequently requires solving large and sparse linear systems. When using the Finite Element Method these systems exhibit a natural block structure that is exploited for efficiency in the “Iterative Solver Template Library” (ISTL). Based on existing sequential preconditioned iterative solvers we present an abstract parallelisation approach ...

Abstract We use the algebraic orthogonality of rotation-free and divergence-free fields in Fourier space to derive solution a class linear homogenization problems as large system. The effective constitutive tensor constitutes only small part vector. Therefore, we propose synchronous local iterative method that is capable efficiently compute single component If convergence solver ensured, i.e., ...

The recent evolution of computers and mathematical programming techniques has provide the development of a new class of algorithms called matheuristics. Associated with an improvement of MIP solvers, many of these methods have been successful applied to solve combinatorial problems. This work presents an approach that hybridizes metaheuristics based on local search and exact algorithms to solve...

Efficient solution methods are investigated in this paper for solving the linear system of equations resulting from the recently developed boundary element method ~BEM! for the coupled structural acoustic analysis @S. H. Chen and Y. J. Liu, J. Acoust. Soc. Am. 106, Pt. 1, 1247–1254 ~1999!#. An iterative solver, namely, the quasiminimal residual method ~QMR!, is selected among others and found t...