We describe and test a software approach to fault detection in common numerical algorithms. Such result checking or algorithm-based fault tolerance (ABFT) methods may be used, for example, to overcome single-event upsets in computational hardware or to detect errors in complex, high-efficiency implementations of the algorithms. Following earlier work, we use checksum methods to validate results returned by a numerical subroutine operating subject to unpredictable errors in data. We consider common matrix and Fourier algorithms which return results satisfying a necessary condition having a linear form; the checksum tests compliance with this condition. We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent in finite-precision floating-point calculations. We concentrate on comprehensively defining and evaluating tests having various accuracy/computational burden tradeoffs, and we emphasize average-case algorithm behavior rather than using worst-case upper, bounds on error.

This is a status report on our progress with the development of PYRAMID, a Fortran 90/95-based library for parallel unstructured adaptive mesh refinement. The library has been designed to simplify the use of adaptive methods in computational science applications by introducing many advanced software engineering features. In this paper, design and performance issues are described concluding with a discussion of our future development plans.

An analysis is presented of the primary factors influencing the performance of a parallel implementation of the UCLA atmospheric general circulation model (AGCM) on distributed-memory, massively parallel computer systems. Several modifications to the original parallel AGCM code aimed at improving its numerical efficiency, load-balance and single-node code performance are discussed. The impact of these optimization strategies on the performance on two of the state-of-the-art parallel computers, the Intel Paragon and Cray T3D, is presented and analyzed. It is found that implementation of a load-balanced FFT algorithm results in a reduction in overall execution time of approximately 45% compared to the original convolution-based algorithm. Preliminary results of the application of a load-balancing scheme for the physics part of the AGCM code suggest that additional reductions in execution time of 10–15% can be achieved. Finally, several strategies for improving the single-node performance of the code are presented, and the results obtained thus far suggest that reductions in execution time in the range of 35–45% are possible. © 1998 John Wiley & Sons, Ltd.

An analysis is presented of several factors influencing the performance of a parallel implementation of the UCLA atmospheric general circulation model(AGCM) on massively parallel computer systems. Several modifications to the parallel AGCM code aimed at improving its numerical efficiency, interprocessor communication cost, load-balance and cache efficiency are discussed. The impact of some of the optimization strategies on the performance of the AGCM code as we implemented on several state-of-the-art parallel computers, including the Intel Paragon, Cray T3D and IBM SP2, is presented and analyzed.

A parallel time-dependent incompressible flow solver and a parallel multigrid elliptic kernel are described. The flow solver is based on a second-order projection method applied to a staggered finite-difference grid. The multigrid algorithms implemented in the elliptic kernel, which is needed by the flow solver, are V-cycle and full V-cycle schemes. A grid-partition strategy is used in the parallel implementations of both the flow solver and the multigrid elliptic kernel on all fine and coarse grids. Numerical experiments and parallel performance tests show the parallel solver package is numerically stable, physically robust and computationally efficient. Both the multigrid elliptic kernel and the flow solver scale very well to a large number of processors on the Intel Paragon and the Cray T3D for computations with moderate granularity. The solver package has been carefully designed and coded so that it can be easily adapted to solving a variety of interesting two and three-dimensional flow problems. The solver package is portable to parallel systems that support MPI, PVM and Intel NX for interprocessor communications.