Optimizing Geometric Multigrid Method Computation Using a
DSL Approach
SessionCompilation Techniques
Event Type
Paper
Compiler Analysis and Optimization
Program Transformation
Programming Language Techniques for Reducing
Energy and Data Movement
Programming Systems
TimeTuesday, November 14th4:30pm -
5pm
Location402-403-404
DescriptionThe Geometric Multigrid (GMG) method is widely used in
numerical analysis to accelerate the convergence of
partial differential equations solvers using a hierarchy
of grid discretizations. Multiple grid sizes and
recursive expression of multigrid cycles make the task
of program optimization tedious. A high-level language
that aids domain experts for GMG and with good
optimization support is thus valuable.
We demonstrate how high performance can be achieved along with enhanced programmability for GMG, with new language/optimization support in the PolyMage DSL framework. We compare our approach with (a) hand-optimized code, (b) hand-optimized code optimized in conjunction with polyhedral techniques, and (c) the existing PolyMage optimizer adapted to multigrid. We use benchmarks varying in multigrid cycle structure and smoothing steps for evaluation. On a 24-core Intel Xeon Haswell multicore system, our automatically optimized codes achieve a mean improvement of 3.2x over straightforward parallelization, and 1.31x over the PolyMage optimizer.
We demonstrate how high performance can be achieved along with enhanced programmability for GMG, with new language/optimization support in the PolyMage DSL framework. We compare our approach with (a) hand-optimized code, (b) hand-optimized code optimized in conjunction with polyhedral techniques, and (c) the existing PolyMage optimizer adapted to multigrid. We use benchmarks varying in multigrid cycle structure and smoothing steps for evaluation. On a 24-core Intel Xeon Haswell multicore system, our automatically optimized codes achieve a mean improvement of 3.2x over straightforward parallelization, and 1.31x over the PolyMage optimizer.
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