Element-wise Implementation of Iterative Solvers for FEM Problems on the Cell Processor

A new implementation of the finite element method(FEM) that is suitable for the Cell processor. Since the Cell processors have a far greater performance and lower byte per-flop (B/F) rate than traditional scalar processors, the amount of memory transfer was reduced and a technique was used to hide the number of memory accesses. The amount of memory transfer was reduced by accepting additional floating-point operations without storing the data if the data were required repeatedly. In the present study, such memory access reduction was applied to the conjugate gradient (CG)method. In order to achieve memory access reduction in the CG method, element-wise computation was used in order to avoid global coefficient matrices, which cause frequent memory accesses. Moreover, all data transfer times are incorporated into the calculation time. As a result, the new implementation performed 10 times better than a traditional implementation run on a PPU.