Terascale Optimal PDE Simulations (TOPS), An Enabling Technology Center Scientific Discovery Through Advanced Computing: Integrated Software Infrastructure Centers
نویسندگان
چکیده
iii 1 Background and Significance 1 2 Preliminary Studies 3 2.1 PDE Time Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 PDE Nonlinear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 PDE-constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Linear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 Eigensystem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Integration and Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.7 Software Performance Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Research Design and Methods 8 3.1 PDE Time Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 PDE Nonlinear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.1 Schwarz Preconditioned Inexact Newton . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.2 Newton-Krylov-Multigrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.3 Nonlinear Multigrid (FAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.4 Common Framework for Three Complementary Approaches . . . . . . . . . . . . . . 10 3.3 PDE-constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3.1 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.3.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 PDE Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4.1 Algebraic Multigrid Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4.2 Geometric Multigrid Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4.3 ILU Preconditioners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4.4 Sparse Direct Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.5 PDE Eigenanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.6 PDE Software Integration and Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.7 PDE Software Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.7.1 Automated Empirical Optimization of Software (AEOS) . . . . . . . . . . . . . . . . 20 3.7.2 Problem-dependent Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.8 Milestones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Consortium Arrangements 24 4.1 Other SciDAC ETCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 SciDAC Application Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3 Internal Collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is sho...
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