COMPUTATION OF ROVIBRATIONAL EIGENVALUES OF VAN-DER-WAALS MOLECULES ON A CRAY T3D

Two algorithms for computing rovibrational eigen solutions fur van der Waals molecules are presented. The performance and scalability of the se algorithms are evaluated on a CRAY T3D with 128 processors using Ar -HO as the test molecule, Both algorithms are based on a discrete vari able 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 Hamiltoni an to obtain the eigenpairs of interest. The second algorithm transfor ms the DVR Hamiltonian using the sequential diagonalization and trunca tion (SDT) approach of Light and co-workers to a reduced order SDT Ham iltonian prior to applying the IRLM. Both algorithms make use of Cheby chev polynomial preconditioning to speed up the convergence of the IRL M. An important factor in the performance of the two algorithms is the efficiency of the matrix-vector product operation. Both algorithms ma ke use of a Sylvester-type transformation to convert most DVR matrix-v ector operations into a series of significantly lower order matrix-mat rix operations, The basic trade-offs between the two algorithms are th at the first algorithm has a significantly higher percentage of level- 3 BLAS operations, which allows it to achieve higher Mflops, whereas t he second algorithm involves the lower order SDT Hamiltonian, which ma kes the IRLM converge faster. The Implementation details (e.g., the di stribution of with the different submatrices that form the tensor repr esentation of the DVR Hamiltonian) are central to achieving maximum ef ficiency and near linear scalability of the algorithms for large value s of the total angular momentum. (C) 1997 Academic Press.