TY - JOUR
T1 - Quantum dynamics on massively parallel computers
T2 - Efficient numerical implementation for preconditioned linear solvers and eigensolvers
AU - Chen, Wenwu
AU - Poirier, Bill
N1 - Funding Information:
This work was largely supported by the Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division of the US Department of Energy under contract DE-FG03-02ER25534. Additional support from The Welch Foundation (D-1523) is also acknowledged. The authors wish to express special gratitude to Michael Minkoff and Albert F. Wagner, whose interest and motivation have made this work possible. Other researchers, notably Tucker Carrington, Jr., Stephen K. Gray, Dinesh K. Kaushik, Dmitry M. Medvedev, Ron Shepard, and Barry F. Smith, are also acknowledged for many stimulating discussions. In addition, we gratefully acknowledge the Jazz Linux Cluster Group of the Mathematics and Computer Science Division at Argonne National Laboratory, for technical support and for the use of the Jazz facility.
PY - 2010/10
Y1 - 2010/10
N2 - The eigenvalue/eigenvector and linear solve problems arising in computational quantum dynamics applications (e.g. rovibrational spectroscopy, reaction cross-sections, etc.) often involve large sparse matrices that exhibit a certain block structure. In such cases, specialized iterative methods that employ optimal separable basis (OSB) preconditioners (derived from a block Jacobi diagonalization procedure) have been found to be very efficient, vis-à-vis reducing the required CPU effort on serial computing platforms. Recently,1,2 a parallel implementation was introduced, based on a nonstandard domain decomposition scheme. Near-perfect parallel scalability was observed for the OSB preconditioner construction routines up to hundreds of nodes; however, the fundamental matrixvector product operation itself was found not to scale well, in general. In addition, the number of nodes was selectively chosen, so as to ensure perfect load balancing. In this paper, two essential improvements are discussed: (1) new algorithm for the matrixvector product operation with greatly improved parallel scalability and (2) generalization for arbitrary number of nodes and basis sizes. These improvements render the resultant parallel quantum dynamics codes suitable for robust application to a wide range of real molecular problems, running on massively parallel computing architectures.
AB - The eigenvalue/eigenvector and linear solve problems arising in computational quantum dynamics applications (e.g. rovibrational spectroscopy, reaction cross-sections, etc.) often involve large sparse matrices that exhibit a certain block structure. In such cases, specialized iterative methods that employ optimal separable basis (OSB) preconditioners (derived from a block Jacobi diagonalization procedure) have been found to be very efficient, vis-à-vis reducing the required CPU effort on serial computing platforms. Recently,1,2 a parallel implementation was introduced, based on a nonstandard domain decomposition scheme. Near-perfect parallel scalability was observed for the OSB preconditioner construction routines up to hundreds of nodes; however, the fundamental matrixvector product operation itself was found not to scale well, in general. In addition, the number of nodes was selectively chosen, so as to ensure perfect load balancing. In this paper, two essential improvements are discussed: (1) new algorithm for the matrixvector product operation with greatly improved parallel scalability and (2) generalization for arbitrary number of nodes and basis sizes. These improvements render the resultant parallel quantum dynamics codes suitable for robust application to a wide range of real molecular problems, running on massively parallel computing architectures.
KW - Quantum dynamics
KW - block Jacobi
KW - chemical physics
KW - eigensolver
KW - linear solver
KW - matrixvector product
KW - parallel computing
KW - preconditioning
KW - sparse matrix
UR - http://www.scopus.com/inward/record.url?scp=78649854773&partnerID=8YFLogxK
U2 - 10.1142/S021963361000602X
DO - 10.1142/S021963361000602X
M3 - Article
AN - SCOPUS:78649854773
SN - 0219-6336
VL - 9
SP - 825
EP - 846
JO - Journal of Theoretical and Computational Chemistry
JF - Journal of Theoretical and Computational Chemistry
IS - 5
ER -