Parallel algorithms of the Purcell method for direct solution of linear systems

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.

Bulk synchronous parallelization of industrial electromagentic software

The parallelization of existing/industrial electromagnetic software using the bulk synchronous parallel (BSP) computation model is presented. The software employs the finite element method with a preconditioned conjugate gradient-type solution for the resulting linear systems of equations. A geometric mesh-partitioning approach is applied within the BSP framework for the assembly and solution phases of the finite element computation. This is combined with a nongeometric, data-driven parallel quadrature procedure for the evaluation of right-hand-side terms in applications involving coil fields. A similar parallel decomposition is applied to the parallel calculation of electron beam trajectories required for the design of tube devices. The BSP parallelization approach adopted is fully portable, conceptually simple, and cost-effective, and it can be applied to a wide range of finite element applications not necessarily related to electromagnetics.

Numerical experiments of some Krylov subspace methods for black oil model

This paper discusses preconditioned Krylov subspace methods for solving large scale linear systems that originate from oil reservoir numerical simulations. Two types of preconditioners, one being based on an incomplete LU decomposition and the other being based on iterative algorithms, are used together in a combination strategy in order to achieve an adaptive and efficient preconditioner. Numerical tests show that different Krylov subspace methods combining with appropriate preconditioners are able to achieve optimal performance.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.

Measuring distributions of jump rates in disordered metal–hydrogen systems by nuclear magnetic relaxation

Monte Carlo calculations of the nuclear magnetic relaxation rate in a disordered metal–hydrogen system having a distribution of jump rates are reported. The calculations deal specifically with the spin-locked rotating-frame relaxation time T1ρ. The results demonstrate that the temperature variation of the rate is only weakly dependent on the distribution and it is therefore unlikely that the jump rate distribution can be extracted from relaxation measurements in which temperature is the main variable. It is shown that the alternative of measuring the relaxation rate over a wide range of spin-locking field strengths at a constant temperature can lead to an evaluation of the distribution.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

A parallel method for solving pentadiagonal systems of linear equations

A new parallel approach for solving a pentadiagonal linear system is presented. The parallel partition method for this system and the TW parallel partition method on a chain of P processors are introduced and discussed. The result of this algorithm is a reduced pentadiagonal linear system of order P \Gamma 2 compared with a system of order 2P \Gamma 2 for the parallel partition method. More importantly the new method involves only half the number of communications startups than the parallel partition method (and other standard parallel methods) and hence is a far more efficient parallel algorithm.

Fitting host-parasitoid models with CV² > 1 using hierarchical generalized linear models

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density–dependent heterogeneity (HDD) to be distinguished from between-patch, host density–independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well–known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.