The numerical solution of partial differential equations using the finite
element method is one of the key applications of high performance computing.
Local assembly is its characteristic operation. This entails the execution of a
problem-specific kernel to numerically evaluate an integral for each element in
the discretized problem domain. Since the domain size can be huge, executing
efficient kernels is fundamental. Their op- timization is, however, a
challenging issue. Even though affine loop nests are generally present, the
short trip counts and the complexity of mathematical expressions make it hard
to determine a single or unique sequence of successful transformations.
Therefore, we present the design and systematic evaluation of COF- FEE, a
domain-specific compiler for local assembly kernels. COFFEE manipulates
abstract syntax trees generated from a high-level domain-specific language for
PDEs by introducing domain-aware composable optimizations aimed at improving
instruction-level parallelism, especially SIMD vectorization, and register
locality. It then generates C code including vector intrinsics. Experiments
using a range of finite-element forms of increasing complexity show that
significant performance improvement is achieved.Comment: Remove volume metadat
