The Multigrid Method. Nicolas Alt n.alt@mytum.de. University of ... (Elliptic) Partial Differential Equation. uxx uyy au = f(x,y) for 0 x,y 1 , a 0 ...
averaging. Linear scalar elliptic PDE. 1 dimension Laplace equation ... Can be well expressed by less variables. Use a coarser level (by choosing every other ...
W. L. Briggs, V. E. Henson, and S F. McCormick, A Multigrid Tutorial, SIAM, ... V. E. Henson, Multigrid for nonlinear problems: an overview, Center for Applied ...
Real-space multigrid methods for DFT and TDDFT: Tuomas Torsti CSC The finnish IT center for Science Laboratory of Physics, Helsinki University of Technology
Improvement of a multigrid solver for 3D EM diffusion ... Introduce (discreet) residu. Goal: solve for r = 0. How? Multigrid solver. Overview Multigrid ...
now possible to simulate flow around an airplane, with engines. first achieved in 1986 ... ( the PDE governing quantum mechanics) to find electron density functions ...
Quad City DJ's, Southern rap group ... Monte Carlo update (Long auto correlations times) ... DMA between GPU on Quad system and network for cluster ...
Recall Big Idea used several times in course. To solve a hard problem, ... 'BR' tire: compute displacement during rolling. Source: Mark Adams, PPPL. 03/14/06 ...
Diagonally dominant. Basic Iterative Methods. Jakobi Method. Model problem. First iteration ... The order of updating is significant. Ascending and descending order ...
A Multigrid Solver for Boundary Value Problems Using Programmable ... General-purpose GPU. Mark Harris. Aaron Lefohn. Ian Buck. Funding. NSF Award #0092793 ...
Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid ... Purcell, et al. 2002. data structures: streams. algorithms: kernels. Concrete model ...
Construct lines of elements based on flow direction ... Strongly convective systems characterized by ... Residual is converged to machine zero on each level (p) ...
BVPs: Background. Boundary value problems are sometimes governed. by PDEs of the form: ... Textures bigger than 2048 on a side. Acknowledgements. Hardware ...
Multi-grid in the Chiral limit. Richard C. Brower. Extreme Scale Computing Workshop ... when tuned further & in chiral limit. Both Domain Wall & Staggered ...
The red points are the ghost points that will be used by the discrete operator. ... Interpolate ghost point(s) for the temporarily corrected solution. ...
A Multigrid Solver for Boundary Value Problems Using Programmable ... General-purpose GPU. Mark Harris. Aaron Lefohn. Ian Buck. Funding. NSF Award #0092793 ...
... 2nd order convergence near holes is impossible or impractical, especially in 3D, ... Error concentrated near holes: Results w/ Extra Smoothing Region. Pre ...
Interpolation Operator. The interpolation operator In(i-1), takes a function on a coarse grid P(i-1) ... In 1D, linearly interpolate nearest coarse neighbors ...
Yeawchu Lee, Harvey Thompson & Phil Gaskell ... Manufacture of photographic film and ink-jet media. Deposition of coatings and inks ink-jet printing ...
Completing the HPCS effort log and background questionnaire. is 5% of hw3 grade (for everyone) For your logs to count in the study you must print & give us a ...
Reduces # stencil coordinates computed per cell. Exposes load reuse to compiler ... memory traffic to 3 load streams per cell. Overhead when switching between ...
20-minute presentation plus 5 minutes for questions. All project members should speak (not ... http://www-sal.cs.uiuc.edu/~steng/talk/3Dmesh/sld001.htm ...
hMETIS ( purely connectivity based ) Random. Distance Information of An Edge ... dij(ll) dij(lr) dij(ul) dij(ur) (1) (2) (3) (4) Experimental Settings. Two ...
Introduction to Scientific Computing II Multigrid Miriam Mehl, Michael Bader Multigrid Algorithm iterate (GS) on the fine grid restrict residual to the coarse ...
Multigrid Overview James Demmel http://www.cs.berkeley.edu/~demmel/ma221/Multigrid.ppt Outline and Review Review Poisson equation Overview of Methods for Poisson ...
Introduction to Scientific Computing II Multigrid Dr. Miriam Mehl Multigrid Algorithm iterate (GS) on the fine grid restrict residual to the coarse grid solve ...
... A. Gupta 04/13/09 CS267 Lecture 20 Multigrid for nonlinear elastic analysis of bone Mechanical testing for material properties ... mathematical properties of T ...
Sorted in two orders (roughly): from slowest to fastest on sequential machines. ... Irregular mesh: Tapered Tube (multigrid) 02/09/05. CS267 Lecture 7. 26 ...
Shock waves in a gas dynamics using AMR (Adaptive Mesh Refinement) See: http: ... Irregular mesh: Tapered Tube (Multigrid) 11/7/09. CS267, Yelick. 29 ...
In previous lesson, we learned some basic knowledge of high ... Jacobi, Gauss-Seidel. Not robust, not efficient. Multigrid, Krylov subspace(CG, GMRES) ...
Future Plans. Documentation, mailing lists, and getting help. ML Package ... Use coarse solves (k 4) to accelerate convergence for A4. Algebraic Multigrid (AMG) ...
Multigrid (next lecture) Reduce to sparse-matrix-vector multiply ... left-to-right row-wise order, we get the Gauss ... above is component-wise multiply. ...
The new multigrid Coulomb method described above allowed tests of the Young ... of electrowetting described below, as well as simulations of electro-osmosis. ...
eliminate new high frequencies. fine grid error. before smoothing. after smoothing ... V-cycle: one recursive call. W-cycle: two recursive calls. F-cycle: ...
High Resolution Aerospace Applications using the NASA Columbia Supercomputer Dimitri J. Mavriplis University of Wyoming Michael J. Aftosmis NASA Ames Research Center
Search in the direction of the gradient of given point (local approximation) ... Multi-Grid. Full Grid. 19. Reference. Numerical Recipe in C. 20. Thank you ...
Discretization of PDE (SiWiR 1) leads to matrix equation Ax = b ... equation A? = r (r is the residual of Ax=b - r = b Ax) ... Of course this is not enough ! ...