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Defining Software Requirements for Scientific Computing

Defining Software Requirements for Scientific Computing. Phillip Colella Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory. High-end simulation in the physical sciences consists of seven algorithms:. Structured Grids (including locally structured grids, e.g. AMR)

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Defining Software Requirements for Scientific Computing

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  1. Defining Software Requirements for Scientific Computing Phillip Colella Applied Numerical Algorithms Group Lawrence Berkeley National Laboratory

  2. High-end simulation in the physical sciences consists of seven algorithms: • Structured Grids (including locally structured grids, e.g. AMR) • Unstructured Grids • Fast Fourier Transform • Dense Linear Algebra • Sparse Linear Algebra • Particles • Monte Carlo Well-defined targets from algorithmic and software standpoint. Remainder of this talk will consider one of them (structured grids) in detail.

  3. Locally-Structured Grid Calculations • Numerical solution represented on a hierarchy of nested rectangular arrays. • Three kinds of computational operations: • Local stencil operations on rectangles. Explicit methods, iterative solvers. • Irregular computation on boundaries. • Copying between rectangles.

  4. Algorithmic Characteristics • O(1) flops per memory access (10 - 100’s). • Codimension one irregularity. • Multiple opportunities for parallelism: within a patch, over patches. • Multiphysics complexity: many different operators acting in sequence on the same collection of state variables (the operators may contain state for performance reasons.) • Irregular computation combined with irregular communication.

  5. Software Characteristics • Layered design to maximize reuse, hide details of parallelism • Rectangular arrays distributed over processers. • Operators to represent the coupling between different levels in the hierarchy. • Solvers, applications. • Fortran 77 on single patches for performance. • Bulk-synchronous SPMD execution, alternates communication / computation. Locally static irregular data distributions, approximately load-balanced. • C++ implementation: extensive use of templates; inheritance used mainly to define interfaces. Irregular computations implemented in C++. O(105) lines of code, supporting a range of applications from cosmology to cell biology. • Prototype Titanium implementation.

  6. What are our problems ? • Mixed-language programming is a maintenance headache. Fortran is a better compromise between expressiveness and performance than C / C++ for multidimensional arrays, but still not entirely satisfactory (no dimension independent syntax). • Bulk-synchronous communication on locally static data distributions limits scalability (Work queues? Overlapping communication and computation?). • Load balancing should be based on runtime measurements, rather than approximate analytical models. • Serial performance issues. Irregular operations written in C++ are not high-performance. O(1) flops / memory access are not a good match for deep memory hierarchies. • Expressiveness and performance are a problem for I/O libraries. • Tool-poor development environment.

  7. Algorithm / Applications Future: More Complexity. • Methods for complex geometry: more irregularity, more complex abstractions. • Hybrid discrete / continuous models: particles, polymers, dynamic surfaces. • Multiple physical processes: widely different workloads on the same grid distributions.

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