Computation of Rovibrational Eigenvalues of van der Waals Molecules on a CRAY T3D

Abstract

Two algorithms for computing rovibrational eigen solutions for van der Waals molecules are presented. The performance and scalability of these algorithms are evaluated on a CRAY T3D with 128 processors using Ar–HO as the test molecule. Both algorithms are based on a discrete variable representation (DVR) of the rovibrational Hamiltonian for van der Waals molecules. The first algorithm applies the implicitly restarted Lanczos method (IRLM) of D. C. Sorensen directly to the DVR Hamiltonian to obtain the eigenpairs of interest. The second algorithm transforms the DVR Hamiltonian using the sequential diagonalization and truncation (SDT) approach of Light and co-workers to a reduced order SDT Hamiltonian prior to applying the IRLM. Both algorithms make use of Chebychev polynomial preconditioning to speed up the convergence of the IRLM. An important factor in the performance of the two algorithms is the efficiency of the matrix–vector product operation. Both algorithms make use of a Sylvester-type transformation to convert most DVR matrix–vector operations into a series of significantly lower order matrix–matrix operations. The basic trade-offs between the two algorithms are that the first algorithm has a significantly higher percentage of level-3 BLAS operations, which allows it to achieve higher Mflops, whereas the second algorithm involves the lower order SDT Hamiltonian, which makes the IRLM converge faster. The implementation details (e.g., the distribution of with the different submatrices that form the tensor representation of the DVR Hamiltonian) are central to achieving maximum efficiency and near linear scalability of the algorithms for large values of the total angular momentum.