1. Bill Appelbe, bill@vpac.org

2. THE SNARK PROJECT Outline • Why do we need another solver? • Design of Snark • Implementation timetable

3. Why Another Solver • No solver meets the requirements we have • The fundamental requirement is that the solver be • Adapt to a wide range problems • Fast (parallel) • Accurate

4. Why Another Solver • Range of problems: • Geological CFD • Mantle convection • Regional crustal deformation • Ore body formation • Tectonic modeling • Multiphase flows • Engineering problems with complex rheologies

5. Design Choices First rule • Decouple, decouple, decouple • Setup of initial conditions • Setup of grid (meshing) • And regriding • Domain decomposition (for scaleable parallelism) • Solver • Should be capable of handing arbitrary material properties • Viewing of output

6. Design Choices Rheology specification User input or another grid format Compiler (Re)-Grid Generator Domain(re)Decompose Solver Engine Viewer

7. Features of Snark • Snark supports the functionality of the ELLIPSIS solver (Moresi) in addition to: • new general purpose parallelexecution • an algebraic multigrid (AMG) technique coupled with the particle-in-cell(PIC) method • Decoupling of equations from generic MG/PIC • Exploit C++ template functions • Generic boundary conditions and grid generator

8. Basic Components of Snark • The Snark system consists of five portable subsystems: • The mesh generator(MGen); • An interface mesh viewer; • The Snark FEM engine; • Resulting data analyzer; and • “Compiler” for rheology specifications • By using well defined API’s, these components can be “plug and play”

9. The Snark Mesh Generator • Generating the FE mesh is the most difficult part of the modeling process; • Mesh design is the most critical decision in FEM+AMG modeling; • The mesh generation needs to reflect the later AMG as well as the parallel algorithms; • The design should consider plugins for versions in the future.

10. The Mesh_Generator(MGen): • 2D and 3D spatial dimensions for the problem domain; • Triangular mesh for 2D and tetrahedral mesh for 3D problems (plug in); • Linear and quadratic (plug in) elements; • Structured mesh; • Isotropic (uniform) mesh; • Adaptive mesh refinement(plug in);

11. How to Develop the MGen? • Based on our comprehensive review of existing mesh generators; • Adapt the features from the existing mesh generators, which are suitable to MGen; • The VPAC in-house expertise in science and engineering as well as software engineering;

12. The First Version: Snark_v1 • The focus of Snark_v1 is to apply the PIC and AMG into the FEM formulation; • Steady state field problems, describing using linear elliptic PDEs; such as • Elasticity; • Heat conduction; • Seepage through porous media; • Irrotational flow of idea fluids; • Distribution of electrical (or magnetic) potential;etc

13. What’s MG and AMG • Multigrid (MG) methods are fast linear iterative solvers based on multilevel, or multiscale paradigm • Two choices: • Geometric vs. Algebraic multigrid • Algebraic multigrid (AMG) methods are any multilevel methods where the geometry is not used (maybe not available) .

14. Why MG (AMG) • MG is amongst the fastest solution techniques known today; • MG can treat arbitrary regions and boundary conditions; • MG directly applies to more complicated situations; • MG exhibits a convergence rate that is independent of the number of the unknowns in the discretized system • MG is amenable to parallel processing

15. Implementation Timetable • First step has been a through organized survey of the literature on available solvers, MG, code, etc. • As an internal website • Delivery of beta of Mgen by the end of 2001 • Couple to the current Ellipsis backend • For feedback and testing • Replace current ellipsis engine by an AMG engine • Mid 2002

16. Related Projects • Platyplus-V2 • A scaleable plate reconstruction tool • In beta release form after 6mo. development • A new generic SPH solver • MNRF and Monash funded • The solvers operate as a “suite” • Snark vs Fastflo • Our aim is performance, parallelism, large problems • Fastflo is aimed at prototyping

17. VPAC HPC Facility • Compaq AlphaServer SC • 32 ES40’s (4 x 833MHz alpha’s, 2G Memory) • Quadrics interconnect (6μsec latency) • 128 processors, • 100+ Gigaflops • 1.4T shared file • server, dual • DLT tapes

18. VPAC HPC Facilities • VPAC “owns” 5% of the cycles of RMIT’s Virtual Reality Centre • For demonstration projects, PR • Tools, training, and support for visualisation

19. Contact Us • Victorian Partnership for Advanced Computing • Website: http://www.vpac.org

20. Acknowledgement Bill Appelbe, Feng Wang, Dev Behera Victorian Partnership for Advanced Computing PO Box 211, Carlton South, Victoria 3053 Louis Moresi and Hans Mühlhaus CSIRO Exploration and Mining, PO Box 437, Nedlands, WA 6009