A Generalised Conjugate Residual method for the solution of non‐symmetric systems of equations with multiple right‐hand sides

This paper presents an iterative algorithm for solving non‐symmetric systems of equations with multiple right‐hand sides. The algorithm is an extension of the Generalised Conjugate Residual method (GCR) and combines the advantages of a direct solver with those of an iterative solver: it does not have to restart from scratch for every right‐hand side, it tends to require less memory than a direct solver, and it can be implemented efficiently on a parallel computer. We will show that the extended GCR algorithm can be competitive with a direct solver when running on a single processor. We will also show that the algorithm performs well on a Cray T3E parallel computer. Copyright © 1999 John Wiley & Sons, Ltd.     

在浅水方程中利用Riemann问题精确解的数值方法

先从一维Riemann问题解的结构入手,分别对湿区和干区两种情况进行分析,得到精确解的解析形式,并讨论其存在性和唯一性,然后采用物理方程旋转不变量的原理,将全局坐标旋转至界面法相的局部坐标,从而将二维浅水方程中的Riemann问题转化为一维问题进行求解。并通过对三个溃坝案例进行数值模拟,证明了在浅水方程中利用Riemann精确解的可行性,验证了该方法在干/湿区问题上的合理性与有效性,也证明此算法具有精确捕捉溃坝波问题的能力。     

ADAPTIVE SOLVER FOR THE p-VERSION OF FINITE ELEMENT METHOD

An adaptive solver for large-scale hierarchic finite element systems has been developed. A decision-making methodology aimed at selecting an optimal solution strategy on the basis of estimated conditioning, sparsity and memory requirements for a given problem has been devised. Numerical experiments have been conducted on selected shell and 3-D problems in the range of 1000–100 000 degrees of freedom. © 1997 by John Wiley & Sons, Ltd.     

Fitting of experimental data using a fractional Kalman-like observer

In this paper, a fractional order Kalman filter (FOKF) is presented, this is based on a system expressed by fractional differential equations according to the Riemann–Liouville definition. In order to get the best fitting of the FOKF, the cuckoo search optimization algorithm (CS) was used. The purpose of using the CS algorithm is to optimize the order of the observer, the fractional Riccati equation and the FOKF tuning parameters. The Grünwald–Letnikov approximation was used to compute the numerical solution of the FOKF. To show the effectiveness of the proposed FOKF, four examples are presented, the brain activity, the cutaneous potential recordings of a pregnant woman, the earthquake acceleration, and the Chua’s circuit response.     

Domain decomposition and multigrid solvers for flow simulation in porous media on distributed memory parallel processors

Realistic simulations of fluid flow in oil reservoirs have been proven to be computationally intensive. In this work, techniques for solving large sparse systems of linear equations that arise in simulating these processes are developed for parallel computers such as INTEL hypercubes iPSC/2 and iPSC/860. This solver is based on a combined multigrid and domain decomposition approach. The Algorithm uses line corrections solved using a multigrid method, line Jacobi and block incomplete domain decomposition as an overall preconditioner for a conjugate gradient-like acceleration method, ORTHOMIN (k). This is shown to be a factor of ten times faster on a 32-processor hypercube compared to widely used sequential solvers. Three test problems are used to validate the results which include implicit wells and faults: The first is based on highly heterogeneous two-phase flow, the second on the SPE Third Comparative Solution and the third on real production compositional data.     

一类非主型方程古沙及柯西问题的解

应用文献提出的双曲型方程的Riemann函数法,并利用超几何函数的特殊性质对一类非主型方程的古沙问题和柯西问题提供求解的方法,给出了解的表达式。     

Implementation of a parallel unstructured Euler solver on shared- and distributed-memory architectures

An efficient three-dimensional unstructured Euler solver is parallelized on a CRAY Y-MP C90 shared-memory computer and on an Intel Touchstone Delta distributed-memory computer. This paper relates the experiences gained and describes the software tools and hardware used in this study. Performance comparisons between the two differing architectures are made.This work was sponsored in part by ARPA (NAG-1-1485) and by NASA Contract No. NAS1-19480 while authors Mavriplis, Saltz and Das were in residence at ICASE, NASA Langley Research Center, Hampton, Virginia. This research was performed in part using the Intel Touchstone Delta System operated by Caltech on behalf of the Concurrent Supercomputing Consortium. Access to this fecility was provided by NASA Langley Research Center and the Center for Research in Parallel Processing. The content of the information does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred.     

A comparison of the different extensions of a weak formulation of an approximate riemann solver for supercritical flows and their relationship to existing schemes

A weak formulation of the Roe linearised Riemann solver proposed recently is examined in the context of the equations governing steady, supercritical flows. Two possible alternatives present themselves, and it is shown that these are equivalent and, moreover, are equivalent to existing schemes.     

DIES：一个领域独立的专家系统

DIES系统是一建造基于知识的自动问题求解器的领域独立专家系统.在该系统中其描述性知识和规范知识(规则)均为知识库中的标准类型项.DIES系统具有双重结构,即认知系统和求解系统,并可满足下列要求。     

A numerical study of combined forced and natural convection heat transfer in a vertical cylinder bundle

Combined forced and natural convection in a bundle of vertical cylinders have been studied numerically with the aid of Riemann geometry. The cylinders heated uniformly are arranged in an equilateral triangular pattern of three bundle spacings S/D = 1.1, 1.5, and 1.9. Numerical calculations are made of the mixed convection of air (Pr = 0.7) in a subchannel of the bundle at ratios of modified Grashof number to Reynolds number Gr*/Re from 1 to 10⁵. The results show that the reverse flows appear along the center line in the subchannel with increasing Gr*/Re. Local Nusselt numbers for the thermally fully‐developed region are well correlated with Gr*/Re. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 639–649, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10118