Optimizing a 3D Multigrid Algorithm for the IA-64 Architecture

Multigrid methods are known to be the numerically most efficient algorithms for solving large linear equation systems. Unfortunately a standard implementation runs with a, compared to the theoretical capabilities of modern processors, disappointing processor efficiency. While it is possible to achieve significant speedups with cache blocking techniques in 2D, 3D problems often don’t benefit from optimizations to the same degree. The IA-64 architecture is a revolutionary new architecture to overcome the problems and limitations of the established dynamically scheduled, speculative execution processors. One of the key concepts is to put large parts of the complexity on the software side, hence the compilers. We present results for an highly optimized multigrid solver in 3D, showing the potential of the IA-64 architecture. Because the compiler is not yet capable to exploit the full potential of the architecture for our type of algorithm the computational intensive parts are implemented in assembly.