Support for Adaptive Computations Applied to Simulation of Fluids in Biological Systems

1. Support for Adaptive Computations Applied to Simulation of Fluids in Biological Systems Kathy Yelick U.C. Berkeley

2. Project Summary • Provide easy-to-use, high performance tool for simulation of fluid flow in biological systems. • Using the Immersed Boundary Method • Enable simulations on large-scale parallel machines. • Distributed memory machine including SMP clusters • Using Titanium, ADR, and KeLP with AMR • Specific demonstration problem: Simulation of the heart model on Blue Horizon.

3. Outline • Generic Immersed Boundary Method in Titanium (IBT) • Titanium status • Immersed Boundary method status • Applications of the method • Heart model • Cochlea model • Future Plans • Data analysis • Solvers

4. Titanium on Blue Horizon • Recent improvements: • Support for PAPI (performance analysis) • Cache optimizations • Portable runtime layer (maintainable) • Faster LAPI-based implementation • Adapted to OS upgrade, ongoing issues • Gcc does not on recent AIX’s • IBM C++ does not fully support templates • Plans • Communication optimizations • Common runtime with UPC (possibly CAF)

5. MPI vs. LAPI on the IBM SP • LAPI bandwidth higher than MPI • Also better small-message overhead • 9usec vs. 11usec • Latest Titanium release leverages this

6. Immersed Boundary Method Structure 4 steps in each timestep Fiber activation & force calculation Fiber Points Interpolate Velocity Spread Force Interaction Navier-Stokes Solver FluidLattice

7. Immersed Boundary Method • Recent Performance Improvements • Use of FFTW in Spectral solver • 10x performance improvement on t3e • Use on BH still pending • Use of scatter/gather communication • Copying bounding boxes is still faster • Depends on application and machine • Load balancing • Alignment of fluid grid (in slabs) and fiber • Multigrid solver might offer more possibilities

8. Load Balancing Fluid grid is divided in slabs for 3D FFT Pizza cutter Egg slicer

9. Application: Heart Simulation • Performance improvements over the last year Heart simulation on a Cray T3E • 64 node t3e ~= 2 node C90 ~= 1-node (8p) BH (probably)

10. Heart Simulation • Recent improvements • Support for heart input • Generate data for NYU visualization • Visualization is now OpenGL (ongoing) • Runs on • Blue Horizon, NERSC SP, T3E, SGI, Millennium • Short term plans • Finish checkpoint/restart • Larger runs • Complete performance model • Validation

11. Cochlea Model • Model of the inner ear • Developed by Julian Bunn and Ed Givelberg • Contains new features, e.g. membranes • Implemented one of these last fall • Plan to have Givelberg here next year

12. Alpha Project Plans • Support for new applications • Berkeley and Michigan • Scaling • Berkeley • Solvers • San Diego, Berkeley, LBNL • Data analysis and model construction • Ohio, Maryland

13. Scallop: Multigrid Poisson Solver • A latency tolerant elliptical solver library • Will be used to build Navier-Stokes Solver • Implemented in KeLP, with a simple interface • Work by Scott Baden and Greg Balls • Based on Balls/Colella algorithm • 2D implementation in both KeLP and Titanium • 3D Solver • Algorithm is complete • Implementation running, but performance tuning is ongoing • Interface between Titanium and KeLP developed

14. Elliptical solvers • A finite-difference based solvers • Good for regular, block-structured domains • Method of Local Corrections • Local solutions corrected by a coarse solution • Good accuracy, well-conditioned solutions • Limited communication • Once to generate coarse grid values • Once to correct local solutions • Trades off extra computation for fewer messages

15. KeLP implementation • Advantages • abstractions available in C++ • built in domain calculus • communication management • numerical kernels written in Fortran • Simple interface • callable from other languages • no KeLP required in user code

16. Improved Heart Structure Model • Current model is • Based on dog heart, textbook anatomy • Approximation by composing cones • Building a more accurate model • Use modern imaging on human heart for model • Need to see individual fibers • Collaboration between • Joel Saltz’s group and • Dr. Robert DePhilip in Anatomy Division of Biomedical Informatics Dept. at Ohio State University • Long term goal • Specialize model to patient using MRI data

17. Analysis of Cardiac Simulations • Methods and tools to analyze 3D datasets from cardiac blood flow. • Outputs are velocity and pressure values on a 3D grid (1283) over many time steps. • Characterize behavior under different pathological and physiological conditions. • Natural and artificial heart valves • Vary the initial values of • Kinematic viscosity • Fluid density • Fiber stiffness and resting lengths • Use parameter study to find conditions that may lead to aneurysm.

18. Analysis of Cardiac Simulations • These queries require support for • spatial subsetting of one or more datasets • processing of the data of interest to visualize and compare results from one or more datasets • execution on high-performance machines and in a distributed environment. • Implemented using DataCutter developed by Joel Saltz’s group.

19. Summary of Alpha Project Impact application data • Several categories • Application development • Heart and cochlea-component simulation • Application-level package • Generic immersed boundary method • Parallel for shared and distributed memory • Enables new larger-scale simulations; finer grid • Solver libraries • Method of Local Corrections • Improved scalability and load balance expected • Data analysis • Building input data and analysis of results software systems