A Fast Wavelet Based Implementation to Calculate Coulomb Potentials on the Cell/B.E.

The calculation of long range interactions is a computationally demanding task in particle based simulations. To reduce the computational complexity from O(N²) to O(N) an algorithm based on a fast 2d-Wavelet transform technique was developed. In this algorithm, a CPU and memory demanding part is to construct the 2d-Wavelet transform of a grid based inverse distance matrix. The 2d-Wavelet transform is thereby calculated via a triple-matrix-multiply and threshold procedure, which results in a sparse representation in Wavelet space. To accelerate the calculation of the triple matrix multiplication, the capabilities of the heterogeneous multicore processor Cell Broadband Engine (Cell/B.E.) are explored. An efficient implementation of the Wavelet transform is developed by considering the architectural requirements of Cell/B.E. Via this implementation, the difficulties and problems in porting code to Cell/B.E. and using sparse linear algebra operations on the processor are assessed.