Partial Differential Equation-Based Applications and Solvers At Extreme Scale

Abstract

Partial differential equation-based applications of multi-scale, multiphysics phenomena have driven the quest for extreme architectural scales since the foundation of modern digital computing and will continue to be principal among a broader set of science drivers for the foreseeable future. However, scientific and engineering drivers ceased long ago to dominate the computing industry and any commercially viable path to the petascale would seem to be through architectures that are assembled from components designed without the balance of resources required by scientific and engineering simulations foremost in mind. Concurrency will be massive and will involve many cores sharing common memory at the finest scales and severely dividing available memory bandwidth. As a result, algorithm designers will have to look beyond the message-passing-based SPMD paradigm that dominates today’s most successful large-scale applications and solver frameworks, with stronger than ever emphasis on locality or operands and synchronization avoidance.

Keywords

extreme scale scientific cyberinfrastructure synchronization-reducing algorithms communication-reducing algorithms

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References

Cai, X.-C. and Keyes, D.E. ( 2002). Nonlinearly preconditioned inexact Newton algorithms , SIAM J. Sci. Comp., 24: 183- 200.

Demmel, J. , Hoemmen, M. , Mohiyuddin, M. , and Yelick, K. ( 2008). Avoiding communication in sparse matrix computations , In: Yang Y and Yuan X (eds) IEEE International Parallel and Distributed Processing Symposium.

Gropp, W. , Haber, E. , Heldmann, S. , Keyes, D. , Miller, N. , Schopf, J. , and Yang, T. ( 2007). Grid-based image registration. In Grid-Based Problem Solving Environments: Implications for Development and Deployment of Numerical Software, edited by P. Gaffney , IFIP Series. NY: Springer, pp. 435-448.

Gropp, W.D. , Kaushik, D.K. , Keyes, D.E. , and Smith, B.F. ( 2001). High performance parallel implicit CFD, Parallel Computing, 27: 337-362.

Keyes, D.E. ( 2003, 2004). A Science-Based Case for Large-Scale Simulation, Volume I, 2003, 76 pp., Volume II, 2004, 303 pp., U.S. Department of Energy Office of Science, http://www.pnl.gov/scales.

Keyes, D.E. , Reynolds, D.R. , and Woodward, C.S. ( 2006). Implicit solvers for large-scale nonlinear problems, J. Phys.: Conf. Ser., 46: 433-442.