Rudnei Dias da Cunha

A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations

We describe the parallelisation of the GMRES(c) algorithm and its implementation on distributed-memory architectures, using both networks of transputers and networks of workstations under the PVM message-passing system. The test systems of linear equations considered are those derived from five-point finite-difference discretisations of partial differential equations. A theoretical model of the computation and communication phases is presented which allows us to decide for which values of the parameterc our implementation executes efficiently. The results show that for reasonably large discretisation grids the implementations are effective on a large number of processors.

Practical CFD Simulations on Programmable Graphics Hardware using SMAC

The explosive growth in integration technology and the parallel nature of rasterization‐based graphics APIs (Application Programming Interface) changed the panorama of consumer‐level graphics: today, GPUs (Graphics Processing Units) are cheap, fast and ubiquitous. We show how to harness the computational power of GPUs and solve the incompressible Navier‐Stokes fluid equations significantly faster (more than one order of magnitude in average) than on CPU solvers of comparable cost. While past approaches typically used Stams implicit solver, we use a variation of SMAC (Simplified Marker and Cell). SMAC is widely used in engineering applications, where experimental reproducibility is essential. Thus, we show that the GPU is a viable and affordable processor for scientific applications. Our solver works with general rectangular domains (possibly with obstacles), implements a variety of boundary conditions and incorporates energy transport through the traditional Boussinesq approximation. Finally, we discuss the implications of our solver in light of future GPU features, and possible extensions such as three‐dimensional domains and free‐boundary problems.

The Parallel Iterative Methods (PIM) package for the solution of systems of linear equations on parallel computers

We present a collection of public-domain Fortran 77 routines for the solution of systems of linear equations using a variety of iterative methods. The routines implement methods which have been modified for their efficient use on parallel architectures with either shared or distributed memory. PIM was designed to be portable across different machines. Results are presented for a variety of parallel computers.

New Parallel (Rank-Revealing) QR Factorization Algorithms

We present a new algorithm to compute the QR factorization of a matrix Am×n intended for use when m ? n. The algorithm uses a reduction strategy to perform the factorization which in turn allows a good degree of parallelism. It is then integrated into a parallel implementation of the QR factorization with column pivoting algorithm due to Golub and Van Loan, which allows the determination of the rank of A. The algorithms were coded in FORTRAN 90 using the MPI library. Results are presented for several different problem sizes on an IBM 9076 SP/2 parallel computer.

A parallel Navier–Stokes solver for the rotating flow problem

In this paper, we investigate the parallel solution of rotating internal flow problems, using the Navier–Stokes equations as proposed by Speziale and Thangam (in 1983) and Speziale (in 1985). A Runge–Kutta time-stepping scheme was applied to the equations and both sequential and message-passing implementations were developed, the latter using MPI, and were tested on a four-processor SGI Origin200 distributed, global shared memory parallel computer and on a 32-processor IBM 9076 SP/2 distributed memory parallel computer. The results show that our approach to parallelize the sequential implementation requires little effort whilst providing good results even for medium-sized problems. Copyright

A benchmark study based on the parallel computation of the vector outer-product A = uvT operation

SUMMARY In this paper we benchmark the performance of the Cray T3D, IBM 9076 SP/1 and Intel Paragon XP/S parallel computers, using implementations of parallel algorithms for the computation of the vector outer-product A = uv T operation. The vector outer-product operation, although very simple in nature, requires the computation of a large number of floating-point operations and its parallelization induces a great level of communication between the processors. It is thus suited to measure the relative speed of the processor, memory subsystem and network capabilities of a parallel computer. It should not be considered a ‘toy problem’, since it arises in numerical methods in the context of the solution of systems of non-linear equations ‐ still a difficult problem to solve. We present algorithms for both the explicit shared-memory and message-passing programming models together with theoretical computation models for those algorithms. Actual experiments were run on those computers, using Fortran 77 implementations of the algorithms. The results obtained with these experiments show that due to the high degree of communication between the processors one needs a parallel computer with fast communications and carefully implemented data exchange routines. The theoretical computation model allows prediction of the speed-up to be obtained for some problem size on a given number of processors. ©1997 by John Wiley & Sons, Ltd.

Sistemas derivados de esquemas nodais em problemas bidimensionais de transporte de partículas: uma análise espectral

Neste trabalho, derivou-se uma abordagem alternativa ao problema de autovalores associado a solucao de um problema bidimensional de transporte de particulas em geometria cartesiana, definido em um dominio retangular, contendo fonte de neutrons isotropica. A abordagem baseia-se no uso de esquemas nodais juntamente com a aplicacao do Metodo de Ordenadas Discretas Analitico (ADO). O esquema nodal e definido em todo o dominio do problema e o metodo ADO e aplicado para desenvolver solucoes para as equacoes integradas. Tal metodologia combinada com o ordenamento das direcoes das particulas, reduz a metade a ordem dos sistemas de autovalores associados, quando comparada a outras abordagens existentes na literatura. Aqui, a estrutura da matriz, no caso de problemas isotopicos, e utilizada para reescrever o problema de forma ainda mais simplificada, como perturbacao de uma matriz diagonal, que por suas caracteristicas inerentes, possibilita ainda maior ganho e eficiencia computacional.

Uma solução particular baseada em funções de Green para formulações nodais derivadas da equação de transporte bidimensional

Neste trabalho, investiga-se um problema de transporte de particulas definido em um dominio retangular com uma fonte de neutrons isotropica, cercado por condicoes de contorno de vacuo em geometria cartesiana bidimensional. A abordagem proposta, ja utilizada anteriormente, reduz a complexidade do modelo bidimensional atraves de esquemas nodais, juntamente com a aplicacao do metodo de ordenadas discretas analitico (ADO). O esquema nodal e definido em todo o dominio do problema e como usualmente em metodos nodais, relacoes entre os fluxos medios e os fluxos desconhecidos nos contornos, sao introduzidos. O metodo ADO e usado para desenvolver solucoes para as equacoes integradas unidimensionais, que sao explicitas em termos das variaveis espaciais. A tecnica utilizada conduz a uma reducao da ordem dos sistemas de autovalores associados, proporcionando desse modo, solucoes de forma mais eficientes no ponto de vista computacional. Para o caso teste aqui analisado, diferentemente de trabalhos anteriores, solucoes particulares mais gerais sao utilizadas baseadas em funcoes de Green.