Parallel computations in quantum Monte Carlo simulation of the van der Waals cluster vibrational eigenstates
The Quantum Monte Carlo computation of the van der Waals cluster vibrational states involves heavy-duty linear algebra computations of large matrices and many iterative procedures containing such computations, which constitute the major bottlenecks of the computational flow. Parallel algorithms can speed up these parts of computations significantly. The study of this dissertation is to parallelize these heavy-duty computations to reduce the overall run time. ^ This thesis first reviews a method to compute the vibrational eigenstates of van der Waals clusters with the Quantum Monte Carlo method, identifies the bottlenecks of the computational flow, introduces the parallel computation facility, and discusses the factors affecting the parallel efficiency. Then it (1) develops routines to solve the overdetermined set of linear equations A(m, k)X(k, n) = B(m, n) with singular value decomposition and in parallel, develops routines to carry out the multiplication of matrices distributed over multiple processors, (2) compares two parallel algorithms to solve the eigenvalue problem: the SVD method and the generalized eigenproblem method, in both speed and accuracy, (3) parallelizes the computations in optimizing the nonlinear coefficients with the Levenberg-Marquardt algorithm. ^ For those heavy-duty computations, the parallel algorithms frequently obtain a speedup of about 10. It is estimated that the overall run time can be reduced by a factor of about 8 when the code is fully parallelized. ^
Physics, Condensed Matter|Computer Science
"Parallel computations in quantum Monte Carlo simulation of the van der Waals cluster vibrational eigenstates"
Dissertations and Master's Theses (Campus Access).