1 / 13

Sparse matrix computations

Sparse matrix computations. Dave O’Hallaron Intel Research Pittsburgh Sept 2007. element. node. t. mesh. simulation results. Galerkin discretization. FEM solver. Animation. Visualization Model. Mathematical Model. Computer Model. Numerical Model. Physical Model. Physical

jaclyn
Download Presentation

Sparse matrix computations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sparse matrix computations Dave O’Hallaron Intel Research Pittsburgh Sept 2007

  2. element node t mesh simulation results Galerkin discretization FEM solver Animation Visualization Model Mathematical Model Computer Model Numerical Model Physical Model Physical System Wave propagation equation Material property model Earthquake ground motion Scientific Computing Process

  3. t Scientific Computing Workflow Physical model Mesh Simulation results Solver Mesh generation Visuali- zation Mesh

  4. David O’Hallaron (CMU CS and ECE) Jacobo Bielak (CMU CivE)

  5. 1994 Northridge Quake Simulation 20 seconds of an aftershock from the Jan 17, 1994 Northridge quake in San Fernando Valley of Southern California.

  6. Teora, Italy 1980

  7. lat. 34.38 long. -118.16 epicenter lat. 34.32 long. -118.48 x San Fernando Valley lat. 34.08 long. -118.75 San Fernando Valley

  8. San Fernando Valley (Top View) Hard rock epicenter x Soft soil

  9. San Fernando Valley (Side View) Soft soil Hard rock

  10. Initial node distribution

  11. Unstructured mesh (top view)

  12. nodes element Partitioned Unstructured Mesh

  13. The disp vector records the displacements of each mesh node during last three timesteps Quake solver code NODEVECTOR3 disp[3], M, C, M23; MATRIX3 K; /* matrix and vector assembly */ FORELEM(i) { ... } /* time integration loop */ for (iter = 1; iter <= timesteps; iter++) { SMVP(K, disp[dispt], disp[disptplus]); disp[disptplus] *= - IP.dt * IP.dt; disp[disptplus] += 2.0 * M * disp[dispt] - (M - IP.dt / 2.0 * C) * disp[disptminus] - ...); disp[disptplus] = disp[disptplus] / (M + IP.dt / 2.0 * C); i = disptminus; disptminus = dispt; dispt = disptplus; disptplus = i; } K is the adjacency matrix of the mesh, a labeled undirected graph 90% of time spent in sparse matrix vector product (SMVP) kernel

More Related