Parallelization and scalability analysis of inverse factorization using the Chunks and Tasks programming model We present three methods for distributed memory parallel inverse factorization of blocksparse Hermitian positive definite matrices. The three methods are a recursive variant of the AINV inverse Cholesky algorithm, iterative refinement, and localized inverse factorization, respectively. All three methods are implemented using the Chunks and Tasks programming model, building on the distributed sparse quadtree matrix representation and parallel matrixmatrix multiplication in the publicly available Chunks and Tasks Matrix Library (CHTML). Although the algorithms are generally applicable, this work was mainly motivated by the need for efficient and scalable inverse factorization of the basis set overlap matrix in large scale electronic structure calculations. We perform various computational tests on overlap matrices for quasilinear Glutamic AcidAlanine molecules and threedimensional water clusters discretized using the standard Gaussian basis set STO3G with up to more than 10 million basis functions. We show that for such matrices the computational cost increases only linearly with system size for all the three methods. We show both theoretically and in numerical experiments that the methods based on iterative refinement and localized inverse factorization outperform previous parallel implementations in weak scaling tests where the system size is increased in direct proportion to the number of processes. We show also that compared to the method based on pure iterative refinement the localized inverse factorization requires much less communication.

Accelerating LargeScale Molecular Similarity Search through Exploiting High Performance Computing Molecular similarity search is a simple but powerful chemoinformatics tool to rapidly find molecules that are structurally similar to a known reference compound from a large molecular database. A variety of indexing structures had been developed to improve the performance of similarity search over the large compound database. However, those algorithms often require a large computational cost to build indices and process queries, especially for a largescale molecular dataset. We study the problem of accelerating similarity search using high performance computing (HPC) and design general algorithms to speed up existing indexing algorithms. We first propose a parallel algorithm based on data chunking, working for all indexing algorithms for similarity search. We theoretically analyze its computation cost and relationships between the speedup and number of data chunks. We further propose a parallel query algorithm for all graphbased indexing algorithms to accelerate their query processing in HPC. Both of our algorithms consistently offer a greater speedup than the baseline algorithm(s) when evaluated with different datasets and parameter settings.