Memory Characteristics of Iterative Methods

Conventional implementations of iterative numerical algorithms, especially multigrid methods, merely reach a disappointing small percentage of the theoretically available CPU performance when applied to representative large problems. One of the most important reasons for this phenomenon is that the current DRAM technology cannot provide the data fast enough to keep the CPU busy. Although the fundamentals of cache optimizations are quite simple, current compilers cannot optimize even elementary iterative schemes. In this paper, we analyze the memory and cache behavior of iterative methods with extensive profiling and describe program transformation techniques to improve the cache performance of two- and three-dimensional multigrid algorithms.