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Scientific Computing

Scientific Computing. Ron Elber. Keshav Pingali. Charlie Van Loan. Steve Vavasis. Time Scale Problems in the Popular Molecular Dynamics Approach. seconds. Action optimization generates approximate trajectories. Channel Gating. Fast folding. Protein Activation. Slow folding.

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Scientific Computing

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  1. Scientific Computing

  2. Ron Elber Keshav Pingali Charlie Van Loan Steve Vavasis

  3. Time Scale Problems in the Popular Molecular Dynamics Approach seconds Action optimization generates approximate trajectories Channel Gating. Fast folding Protein Activation Slow folding Mol. Dyn.

  4. Initial value solution versus optimization of an action • Interpolate to next coordinate based on previous coordinate and velocity vectors • Optimize a current guess for the whole trajectory starting from an initial guess

  5. Cytochrome c folding: a millisecond (10-3 seconds) process with the Stochastic Difference Equation (SDE) Straightforward molecular dynamics can do 10-7 seconds

  6. Mobile Computational Grid Programs • Programs run for many hours on large machines • with hundreds of processors. • -Mobile programs can adapt to changing resource • availability by migrating to new sites on grid. • -New site may have different number and type of • processors. • Goal: programs  mobile programs in a • semi-automatic way.

  7. Programs  Mobile Programs • Solution: program transformation • Insert code for saving/restoring application state (done by C3 compiler) • Use type information to reconstruct state at remote site • Applications become “self-checkpointing” and “self-restarting” • Application-level checkpointing (ALC) (cf. system-level checkpointing) • Efficient • 5% overhead or less for sequential codes • About 10% for MPI codes (homogeneous platforms)

  8. Ongoing Work • Program analysis to reduce the amount of saved state • Joint work with Radu Rugina • Heterogeneous platforms • Different architectures • Different number of processors • Self-optimization • Other applications: • Speculative computation • Backward differentiation

  9. Real-Time Matrix-based Signal Processing • Repeat in real time: • Sense atmosphere • Solve matrix problem • Refocus deformable • mirror Maximize trace of U1T A1U1 + … + UkTAk Uk where A1 ,…, Ak are symmetric matrices and U = [ U1 | … | Uk ] is orthogonal.

  10. Mesh Generation & Guaranteed-Quality Triangulation • Problem: Given a description of a 2D or 3D geometric set, produce a subdivision into triangles or tetrahedra • First guaranteed solution to 2D problem uses constrained Delaunay triangulation (Chew, 1989) • Shewchuk’s high-quality implementation of these ideas won 2003 Wilkinson prize.

  11. 2D Delaunay Mesh • Each triangle has the empty circle property

  12. 3D Delaunay Mesh • Empty sphere property holds but does not imply a quality mesh • Some fixes in the literature, but it seems like a new idea is needed • Alternative: hierarchical space decomposition • QMG (Mitchell & Vavasis 2000) • New algorithm based on longest edge bisection

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