title: Semiempirical Molecular Dynamics (SEMD) I: Midpoint-Based Parallel Sparse Matrix-Matrix Multiplication Algorithm for Matrices with Decay.
abstract: In this paper, we present a novel, highly efficient, and massively parallel implementation of the sparse matrix-matrix multiplication algorithm inspired by the midpoint method that is suitable for matrices with decay. Compared with the state of the art in sparse matrix-matrix multiplications, the new algorithm heavily exploits data locality, yielding better performance and scalability, approaching a perfect linear scaling up to a process box size equal to a characteristic length that is intrinsic to the matrices. Moreover, the method is able to scale linearly with system size reaching constant time with proportional resources, also regarding memory consumption. We demonstrate how the proposed method can be effectively used for the construction of the density matrix in electronic structure theory, such as Hartree-Fock, density functional theory, and semiempirical Hamiltonians. We present the details of the implementation together with a performance analysis up to 185,193 processes, employing a Hamiltonian matrix generated from a semiempirical NDDO scheme.
authors.forename: Valéry
authors.initials: V
authors.lastname: Weber
authors.affiliation: IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland.
authors.forename: Teodoro
authors.initials: T
authors.lastname: Laino
authors.affiliation: IBM Systems Lab Services Russia/CIS, Presnenskaya Nab., 10, 123317, Moscow, Russia.
authors.forename: Alexander
authors.initials: A
authors.lastname: Pozdneev
authors.affiliation: IBM Science and Technology Center, Presnenskaya Nab., 10, 123317, Moscow, Russia.
authors.forename: Irina
authors.initials: I
authors.lastname: Fedulova
authors.affiliation: IBM Research-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Curioni
mesh_terms: D000465:Algorithms; D056004:Molecular Dynamics Simulation; D011789:Quantum Theory; D055672:Static Electricity