Basic linear parallel solver for large CFD applications using decomposed unstructured meshes

A distributed Java platform has been designed and built for the simplified implementation of distributed Java applications. Its programmable nature means that code as well as data is distributed over a network. The platform is largely based on the Java Distributed Computation Library of Fritsche, Power, and Waldron. The generality of our system is demonstrated through the emulation of a MIMD (multiple instruction, multiple data) architecture. This is achieved by augmenting the server with a virtual pipeline processor. We explain the design of the system, its deployment over a university network, and its evaluation through a sample application.KeywordsData UnitClient SoftwareMultiple InstructionObject ArrayPipeline ProcessorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Parallel solution methods for the Navier-Stokes equations

The performance of large-scale real-world applications may be enhanced by more efficient utilization of today's powerful parallel computing hardware. The authors describe a novel MIMD (multiple instruction, multiple data) static task allocation methodology created to achieve this goal for a wide range of real-time and deterministic systems. The method performs automatic assignment, mapping, and scheduling of the executable tasks to the available set of processors, assuming synchronous nonbuffered (lock-step) communication between the sending and receiving processors and an arbitrary static message-passing topology. The algorithm incorporates a set of list-based heuristics and graph-theoretical procedures designed to balance computational load with communication requirements. The effectiveness of the method has been verified by applying it to a large number of randomly generated task systems that span a wide range of inherent concurrency as well as to a task system of a real-world simulation of the Space Shuttle main rocket engine. >

On Factors Limiting the Generation of Efficient Compiler-Parallelized Programs

When using MIMD (multiple instruction, multiple data) parallel computers, one is often confronted with solving a task composed of many independent subtasks where it is necessary to synchronize the processors after all the subtasks have been completed. This paper studies how the subtasks should be allocated to the processors in order to minimize the expected time it takes to finish all the subtasks (sometimes called the makespan). We assume that the running times of the subtasks are independent, identically distributed, increasing failure rate random variables, and that assigning one or more subtasks to a processor entails some overhead, or communication time, that is independent of the number of subtasks allocated. Our analyses, which use ideas from renewal theory, reliability theory, order statistics, and the theory of large deviations, are valid for a wide class of distributions. We show that allocating an equal number of subtasks to each processor all at once has good efficiency. This appears as a consequence of a rather general theorem which shows how some consequences of the central limit theorem hold even when we cannot prove that the central limit theorem applies.

The application of parallel computers to reservoir simulation is studied with the aid of two recently introduced Multiple Instruction, Multiple Data (MIMD) computers. The problems posed by reservoir simulators are shown to be particularly well suited for such parallel computers* Fundamental parallel programming techniques using Fortran are presented for the Hetrogeneous Element Processor (HEP) produced by Denelcor and the iPSC Hypercube produced by Intel. These techniques are then applied to two of the most time consuming tasks in reservoir simulation: forming the matrix coefficients and producing a sparse matrix solution. The problem of parallel formation of sparse matrix coefficients is addressed for the single and multiphase cases using both black oil and compositional fluid models. Parallel sparse matrix solution is addressed by considering D4 ordered Gaussian elimination, and the multigrid, conjugate gradient, and Successive Over-Relaxation (SOR) methods. Three parallel algorithms based on SOR are developed to illustrate the possible diversity of parallel algorithms. The red-black and multicolored SOR methods which are often used on vector machines are shown to be easily adaptable to parallel MIMD machine. Matrix partitioning and a new method of iteration pipelining are also presented as parallel SOR methods. The various SOR algorithms, in parallel form, are mapped onto the HEP to illustrate the speedups currently possible on an MIMD machine. Projections are made on the future importance of these types of machines to reservoir simulation.

An efficient parallel model for coastal transport process simulation

Recently, use of parallel machines in reservoir simulation has received considerable attention from the petroleum industry. This paper presents parallelization of a 3D compositional, equation-of-state reservoir simulator on the CM-5 and KSR-1. To the best of our knowledge, this is the first time that the parallelization of a compositional reservoir simulator has been performed on both the CM-5 and KSR-1. For new users of the CM-5 machines, the software and hardware of CM-5 architecture is presented, as well as details of the parallelization techniques. For example, domain decomposition, I/O's, phase equilibrium computations, and well model are described. The parallelism techniques on the KSR-1 are presented with the emphasis on the porting of the phase equilibrium calculation. The performance of each machine is evaluated by showing the speedup on different sets of processing nodes. Two test problems were used to explore the capability of the parallelized version of the code; one is a waterflood problem and the other is a CO2 multiple contact miscible flood, both in a West Texas oil field. These field problems were run on 1, 2, 4, 8, 16, and 32 processors to get insight into the locations of communication bottlenecks, generally occurring in the programming with distributed memory machines. The problems of latency and bandwidth which are associated with communication efficiency of the CM-5 are also addressed.

A numerical implementation of the Domain Decomposition (DD) method for parallel computation of time-harmonic waves is presented. The Finite Element method on unstructured mesh is employed to discretize the boundary-value problem. A nonover-lapping mesh partitioning is used to build an overlapping domain decomposition. The algorithm also defines the new subdomain boundaries, other than the original boundaries of the global computational domain, on which transmission conditions are introduced. The independent subdomain problems can be solved concurrently, one problem per processor, on a parallel computer. The iterative scheme used to update the subdomain transmission conditions is computationally efficient and only swaps the nodal values in the overlapping region between adjacent subdomains. For exterior problems, the communication required to update the conditions on the outer boundary is substantially reduced by employing a modified Dirichlet-to-Neumann (DtN) map with truncated support. Numerical results are presented for a radiation model problem. It is shown that the DtN nonreflecting conditions eliminate spurious reflections and that the iterative scheme leads to a continuous global solution. The DD algorithm also has a very good convergence rate and significantly reduces memory requirement in comparison with a direct solver.

Recent years have seen the upraising of a new type of processors strongly relying on the Single Instruction, Multiple Data (SIMD) architectural principle. The main idea behind SIMD computing is to apply a flow of instructions to multiple pieces of data in parallel and synchronously. This permits the execution of thousands of operations in parallel, achieving higher computational performance than with traditional Multiple Instruction, Multiple Data (MIMD) architectures. The level of parallelism required in SIMD computing can only be achieved in image coding systems via microscopic parallel strategies that code multiple coefficients in parallel. Until now, the only way to achieve microscopic parallelism in bit plane coding engines was by executing multiple coding passes in parallel. Such a strategy does not suit well SIMD computing because each thread executes different instructions. This paper introduces the first bit plane coding engine devised for the fine grain of parallelism required in SIMD computing. Its main insight is to allow parallel coefficient processing in a coding pass. Experimental tests show coding performance results similar to those of JPEG2000.

In this paper a new strategy is presented how a direct simulation of aeroacoustical problems becomes feasible. The key idea is to introduce a heterogeneous domain decomposition. The whole computational domain is sub-divided into smaller domains. In each of these sub-domains the equations, the discretization, the mesh and the timestep may change and are adapted to the local behavior of the solution. To reduce the total number of points we propose the use of high order methods. Here the class of ADER-Finite Volume schemes on structured meshes and ADER-Discontinuous Galerkin methods on unstructured meshes are a good choice. Numerical results for the Single Airfoil in Gust Response Problem from the 4th CAA Workshop on Benchmark Problems are presented.

A staggered space–time discontinuous Galerkin method for the incompressible Navier–Stokes equations on two-dimensional triangular meshes

A simple weighted essentially non-oscillatory limiter for the correction procedure via reconstruction (CPR) framework on unstructured meshes

Department of Computing Science, Chalmers University of Technology, S-41296 G¨oteborg, Sweden,lindskog@cs.chalmers.seFinite element meshes and nodenumberingssuitable for parallel solution with equally loaded processors are pre-sented for linear orthotropic elliptic partial differential equations. These problems are of great importance for in-stance in oil and airfoil industry. The linear systems of equations are solved by the conjugate gradient methodpreconditionedby modified incompletefactorization, MIC.The basic method presented,is based on fronts of un-coupled nodes and unlike earlier methods it has the advantage of no requirement of a specific orientation of themesh. This method is howeverin generalrestricted to small degreeof anisotropyin the differential equation. An-other method, which does not suffer from this limitation, uses rotation of the differential equation and spectralequivalence.Therotation is madein such a way that in thenew coordinatesystem, thebasic methodis applicable.The spectral equivalence property is used for estimation of the condition number of the preconditioned system.Both methods are suitable for implementation on parallel computers. The computer architecture could be singleinstruction multiple data (SIMD) as well as multiple instruction multiple data (MIMD) with shared or distributedmemory.Implementation ofthe basicmethodon a sharedmemory parallelcomputershowsasignificantimprove-ment by use of the MIC method compared to the diagonalscaling preconditioningmethod.

A large variety of multiple instruction, multiple data (MIMD) parallel machines-some with global shared memory and some without, some with few processors to some with a few thousand processors-are becoming commercially available, and more are being proposed, designed, or developed. Programming such machines for fast execution of desired applications remains a challenging problem. An examination is made of some broad approaches towards this goal, identifying relevant issues and presenting a few guidelines that should be helpful in parallel programming research and development. The Chare Kernel parallel programming system is proposed as a solution to the parallel programming problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>