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The purpose of this paper is to improve the performance of block-multicolor (BMC) ordering for the parallelized incomplete-Cholesky-preconditioned conjugate gradient (ICCG) method. Then, the BMC ordering based on level structure arising in reverse Cuthill-McKee RCM ordering is newly proposed. The name of proposed method is abbreviated as “RBMC”. This paper shows the validity of proposed method by comparison with greedy-based multicolor (MC) and conventional BMC on the real symmetric linear system derived from the voltage-driven finite element method in time domain.

In RBMC, the blocking and coloring is performed level by level. The number of synchronizations in forward and backward substitution is reduced so that all blocks can be colored with two colors. However, the load-balance in forward and backward substitution might deteriorate because the irregular block matrices are distributed around diagonal. To uniformize load-balance in forward and backward substitution, the RBMC combined with the concept of block red-black ordering has been developed.

The modified RBMC was the most effective for reduction of the elapsed time among four orderings (MC, BMC, RBMC, modified RBMC) owing to improvement of convergence characteristic and load-balance.

The proposed method had two advantages: although the number of unknowns per block must be previously determined in BMC, its parameter is automatically determined in proposed method, the number of synchronization in forward and backward substitution can be reduced.

We show how to quickly estimate spatial probit models for large data sets using maximum likelihood. Like Beron and Vijverberg (2004), we use the GHK (Geweke-Hajivassiliou-Keane) algorithm to perform maximum simulated likelihood estimation. However, using the GHK for large sample sizes has been viewed as extremely difficult (Wang, Iglesias, & Wooldridge, 2013). Nonetheless, for sparse covariance and precision matrices often encountered in spatial settings, the GHK can be applied to very large sample sizes as its operation counts and memory requirements increase almost linearly with n when using sparse matrix techniques.

A new algorithm for reducing the profile and root‐mean‐square wavefront of sparse matrices with a symmetric structure is presented. Our numerical experiments show an overall better performance than the widely used reverse Cuthill‐McKee, Gibbs‐King and Sloan algorithms. The new algorithm is fast, simple and useful in engineering analysis where it can be employed to derive efficient orderings for both profile and frontal solution schemes.

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.

To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.

Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.

The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

The minimum profile problem of a sparse matrix is theoretically treated, and by using the results a new profile reducer is proposed. Numerical experiments clarify that the new reducer is effective for the node re‐ordering of graphs with rather complex configuration. Further considerations on the proposed method and numerical error of the skyline method are also given.

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.

This paper aims to investigate thermal geometric optimisation of rectangular heat conductive cooling structures within solid heat‐generating media for the purpose of minimising peak temperatures and enabling optimum use of spatial volume within integrated power electronics.

A vortex‐centred finite volume numerical solver was developed, employing a fully implicit solution algorithm to obtain 3D temperature distributions. By comparing the peak temperatures obtained for a wide range of related cases, optimised cross‐sectional shapes for particular input conditions were obtained.

Optimum shapes are dependent on seven identified parameters. In cases where a low percentage of volume is occupied by cooling structures, a high tendency exists for continuous thin cooling layers, as opposed to discrete rectangular cooling inserts, to present the best thermal behaviour. At higher volume percentages, the opposite is true.

The reduced dimensions of cooling inserts have caused manufacturability to be a concern. Research has shown that at small dimensional scale ranges the cross‐sectional shape of the cooling insert has little influence on its thermal performance. In such cases little or no thermal advantage or loss is incurred by making use of continuous cooling layers, which are easiest to manufacture.

The tendencies of optimum cooling structure shapes were obtained and described in terms of seven geometric and material property‐related parameters. Thermal performance of individual inserts is not linearly proportional to dimensional scaling and it was found that, at small‐scale ranges, optimisation from a manufacturing viewpoint would not significantly impact on thermal performance.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

This paper develops C++ and Fortran-90 solvers to establish parallel solution procedures in a finite element or meshless analysis program using shared memory computers. The paper aims to discuss these issues.

The stiffness matrix can be symmetrical or unsymmetrical, and the solution schemes include sky-line Cholesky and parallel preconditioned conjugate gradient-like methods.

By using the features of C++ or Fortran-90, the stiffness matrix and its auxiliary arrays can be encapsulated into a class or module as private arrays. This class or module will handle how to allocate, renumber, assemble, parallelize and solve these complicated arrays automatically.

The source codes can be obtained online at http//myweb.ncku.edu.tw/∼juju. The major advantage of the scheme is that it is simple and systematic, so an efficient parallel finite element or meshless program can be established easily.

With the minimum requirement of computer memory, an object-oriented C++ class and a Fortran-90 module were established to allocate, renumber, assemble, parallel, and solve the global stiffness matrix, so that the programmer does not need to handle them directly.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.