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1.
The incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method. 相似文献
2.
This paper is concerned with the parallel implementation of the incomplete factorization preconditioned iterative method. Although the use of such parallel ordering as multicolor ordering may increase parallelism in factorization, it often slows convergence when used in the preconditioned method, and thus may offset the gain in speed obtained with parallelization. Further, the higher the parallelism of an ordering, the slower the convergence; the lower the parallelism, the faster the convergence. This well-known trade-off between parallelism and convergence is well explained by the property of compatibility, the level of which can be clearly seen when ordering is presented in graph form (S. Doi, A. Lichnewsky, A graph-theory approach for analyzing the effects of ordering on ILU preconditioning, INRIA report 1452, 1991). In any given method, the fewer the incompatible local graphs in an ordering (i.e., the lower the parallelism), the faster the convergence (S. Doi, Appl. Numer. Math. 7 (1991) 417–436; S. Doi, in: T. Nodera (Ed.), Advances in Numerical Methods for Large Sparse Sets of Linear Systems, 7 Keio University, 1991). An ordering with no incompatible local graphs, for example, such as that implemented on vector multiprocessors by using the nested dissection technique, will have excellent convergence, but its parallelism will be limited (S. Doi, A. Lichnewsky, Int. J. High Speed Comput. 2 (1990) 143–179). To attain a better balance, a certain degree of incompatibility is necessary. In this regard, increasing the number of colors in multicolor ordering can be a useful approach (S. Fujino, S. Doi, in: R. Beauwens (Ed.), Proceeding of the IMACS Internation Symposium on Iterative Methods in Linear Algebra, March 1991; S. Doi, A. Hoshi, Int. J. Comput. Meth. 44 (1992) 143–152). Two related techniques also presented here are the overlapped multicolor ordering (T. Washio, K. Hayami, SIAM J. Sci. Comput. 16 (1995) 631–650), and a fill-in strategy selectively applied to incompatible local graphs. Experiments conducted with an SX-5/16A vector parallel supercomputer show the relative effectiveness of increasing the number of colors and also of using this approach in combination with overlapping and with fill-ins. 相似文献
3.
《国际计算机数学杂志》2012,89(5):583-594
Modelling the interaction of an acoustic field in a fluid and an elastic structure submerged in the fluid leads to a system of complex linear equations with a complicated sparsity structure and, for higher wavenumbers and adequate modelling, the systems are very large. Direct methods are not practical. Preconditioned iterative methods, which are suitable for single operator equations, are not immediately applicable to the coupled case. This article proposes a block diagonal preconditioner of the sparse approximate inverse (SPAI) type that can accelerate the convergence of Krylov iterative solvers for the coupled system. Moreover, the proposed preconditioner can properly and implicitly scale the coupled matrix. Some numerical results are presented to demonstrate the effectiveness of the new method. 相似文献
4.
Normalized explicit approximate inverse matrix techniques for computing explicitly various families of normalized approximate inverses based on normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference and finite element discretization of partial differential equations are presented. Normalized explicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of linear and non-linear systems. Theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also presented. Applications of the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given. 相似文献