### LANS Publications

# "Improving the performance of tensor matrix vector multiplication in cumulative reaction probability based quantum chemistry codes"

D. K. Kaushik, W. D. Gropp, M. Minkoff, and B. F. Smith

Preprint ANL/MCS-P1533-0808

Preprint Version: [pdf]

Cumulative reaction probability (CRP) calculations provide a viable computational approach to estimate reaction rate coefficients. However, in order to give meaningful results these calculations should be done in many dimensions (ten to fifteen). This makes CRP codes memory intensive. For this reason, these codes use iterative methods to solve the linear systems, where a good fraction of the execution time is spent on matrix-vector multiplication. In this paper, we discuss the tensor product form of applying the system operator on a vector. This approach shows much better performance and provides huge savings in memory as compared to the explicit sparse representation of the system matrix.