A novel parallel algorithm for large‐scale Fock matrix construction with small locally distributed memory architectures: RT parallel algorithm

Abstract

We developed a novel parallel algorithm for large-scale Fock matrix calculation with small locally distributed memory architectures, and named it the "RT parallel algorithm." The RT parallel algorithm actively involves the concept of integral screening, which is indispensable for reduction of computing times with large-scale biological molecules. The primary characteristic of this algorithm is parallel efficiency, which is achieved by well-balanced reduction of both communicating and computing volume. Only the density matrix data necessary for Fock matrix calculations are communicated, and the data once communicated are reutilized for calculations as many times as possible. The RT parallel algorithm is a scalable method because required memory volume does not depend on the number of basis functions. This algorithm automatically includes a partial summing technique that is indispensable for maintaining computing accuracy, and can also include some conventional methods to reduce calculation times. In our analysis, the RT parallel algorithm had better performance than other methods for massively parallel processors. The RT parallel algorithm is most suitable for massively parallel and distributed Fock matrix calculations for large-scale biological molecules with more than thousands of basis functions.

Parallel Fock matrix construction program for molecular orbital calculation—Specific computer with a hierarchical network

“…19 Using estimation of overlap integrals, many CS pairs are screened out from the Fock matrix construction of a large molecular system. The number of survived CS pairs is kept small (O(N)) in a large molecular system, 14 and it is useful to make a surviving CS-pair table before Fock matrix construction.…”

“…To perform an MO calculation for a large-size molecule, many parallelization algorithms for PC clusters have been proposed, and present successive parallelization efficiencies with dynamic load-balancing (DLB) schemes. [11][12][13][14] Under the hierarchical network architecture, the overhead of communication between processors could become large, which would make it difficult to apply these previous DLB parallel algorithms to the system. In this article, we propose parallel Fock matrix construction algorithm on the hier-archical network architecture and implement it into the GAMESS program 15 on an EHPC evaluation system, which is a system to evaluate parallelized software for EHPC system architecture without making an actual special-purpose LSI.…”

Parallel Fock matrix construction with distributed shared memory model for the FMO‐MO method

“…By now, several distributed parallel direct Fock matrix construction algorithms have been proposed. [12][13][14][15] Harrison et al have developed a parallel algorithm 14 for distributed storage using the Global Array (GA) toolkit, 16 where Fock and density matrices are held in distributed shared memory of the GA. As the GA has several useful functionalities, such as non-blocking asynchronous remote memory access (RMA), atomic increment of global counter and so on, it has been utilized in a variety of computational chemistry packages for efficiently distributed parallel algorithms with dynamic loadbalancing. They have reported good parallel efficiency for middle sized molecules with atom-blocked/dynamically-blocked parallel algorithms.…”

Parallel algorithm for the computation of the Hartree-Fock exchange matrix: Gas phase and periodic parallel ONX

“…[28][29][30][31][32][33][34] Most of the current parallel methods are based on an integral driven strategy to compute the Fock matrix. On one side, the integral driven approach allows an efficient and simple way to use the full permutational symmetry of the two electron integrals, reducing considerably the computational time.…”

“…5 The parallelization of the later requires expensive communications of data as do conventional algorithms. 33 The paper is organized as follows: In Sec. II the method will be outlined.…”