摘要:

AbstractThe problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope‐reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2‐sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reording algorithm usually computes smaller envelope sizes than those obtained from the current standards such as the Gibbs—Poole—Stockmeyer (GPS) algorithm or the reverse Cuthill—McKee (RCM) algorithm in SPARSPAK, in some cases reducing the envelope by more than a fact

ISSN:1070-5325    

DOI:10.1002/nla.1680020402

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractWe show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M‐matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are include

ISSN:1070-5325    

DOI:10.1002/nla.1680020403

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe application of some recently proposed algebraic multilevel methods for the solution of two‐dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming pape

ISSN:1070-5325    

DOI:10.1002/nla.1680020404

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper presents a general method to associate the operator splitting for the Peaceman—Rachford procedure with a decomposition of the domain in problems arising from finite element discretization of partial differential equations. The algorithm is provably convergent without any symmetry requirement. Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman—Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher‐dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial ma

ISSN:1070-5325    

DOI:10.1002/nla.1680020405

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020406

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020401

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY