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4 projects in high energy and nuclear physics

&. 4 projects in high energy and nuclear physics. 14 projects in biological and environmental research. PDEs. are dense. in the SciDAC. & ISICs. 10 projects in basic energy sciences. 5 projects in fusion energy science. portfolio.

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4 projects in high energy and nuclear physics

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  1. &

  2. 4 projects in high energy and nuclearphysics 14 projects in biological and environmental research PDEs are dense in the SciDAC & ISICs 10 projects in basic energy sciences 5 projects in fusion energy science portfolio “The partial differential equation entered theoretical physics as a handmaid, but has gradually become mistress.” – A. Einstein

  3. Optimizer Sens. Analyzer Time integrator Nonlinear solver Eigensolver Linear solver Indicates dependence Scope for TOPS • Design and implementation of “solvers” for PDE-derived systems • Linear solvers • Eigensolvers • Nonlinear solvers • Time integrators • Optimizers • Software integration • Performance optimization (w/ sens. anal.) (w/ sens. anal.)

  4. Status of CMRS-TOPS collaboration • CMRS team has provided TOPS with discretization of model 2D multicomponent Hall magnetic reconnection evolution code in PETSc’s DA/DMMG format, using automatic differentiation for Jacobian objects • TOPS has implemented fully nonlinearly implicit Newton-GMRES-MG-SOR parallel solver (with deflation of nullspace in CMRS’s doubly periodic formulation) • Both first- and second-order implicit temporal integration available • CMRS and TOPS reproduce the same dynamics on the same grids with the same time-stepping, up to a finite-time singularity due to collapse of current sheet (that falls below presently uniform mesh resolution) • TOPS code, being implicit, can choose timesteps an order of magnitude larger, with potential for higher ratio in more physically realistic parameter regimes, though it is slower in wall-clock time for small CFL • Plan: tune PETSc solver by profiling, blocking, reuse, etc. • Plan: identify the numerical complexity benefits from implicitness (in suppressing fast timescales) and quantify (explicit versus implicit) • Plan (with APDEC team): incorporate AMR

  5. Vorticity, early time Vorticity, later time zoom 2D Hall MHDsawtooth instability (PETSc examples /snes/ex29.c and /sles/ex31.c) (Porcelli et al., 1993, 1999) Model equations: Equilibrium: figures c/o A. Bhattacharjee, CMRS

  6. PETSc’s DMMG in Hall MR application • Mesh and time refinement studies of CMRS Hall magnetic reconnection model problem (4 mesh sizes, dt=0.1 (near CFL limit for fastest wave) on left, dt=0.8 on right) • Measure of functional inverse to thickness of current sheet versus time, for 0<t<200 (nondimensional), where singularity occurs around t=215

  7. PETSc’s DMMG in Hall MR app., cont. • Implicit timestep increase studies of CMRS Hall magnetic reconnection model problem, on finest (192192) mesh of previous slide, in absolute magnitude, rather than semi-log

  8. Newton nonlinear solver asymptotically quadratic Krylov accelerator spectrally adaptive Schwarz preconditioner parallelizable Newton-Krylov-Schwarz – a parallel PDE “workhorse”

  9. CMRS/PETSc Library Interactions Main Routine Timestepping Solvers (TS) Nonlinear Solvers (SNES) Linear Solvers (SLES) PETSc PC KSP Application Initialization Function Evaluation Jacobian Evaluation Post- Processing CMRS code PETSc code ADIC generated code

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