title: Parallel implementation of a direct method for calculating electrostatic potentials.
abstract: The authors present a method for calculating the electrostatic potential directly in a straightforward manner. While traditional methods for calculating the electrostatic potential usually involve solving the Poisson equation iteratively, the authors obtain the electrostatic interaction potential by performing direct numerical integration of the Coulomb-law expression using finite-element functions defined on a grid. The singularity of the Coulomb operator is circumvented by an integral transformation and the resulting auxiliary integral is obtained using Gaussian quadrature. The three-dimensional finite-element basis is constructed as a tensor (outer) product of one-dimensional functions, yielding a partial factorization of the expressions. The resulting algorithm has, without using any prescreening or other computational tricks, a formal computational scaling of Omicron(N4/3), where N is the size of the grid. The authors show here how to implement the method for efficiently running on parallel computers. The matrix multiplications of the innermost loops are completely independent, yielding a parallel algorithm with the computational costs scaling practically linearly with the number of processors.
authors.affiliation: Department of Chemistry, University of Tromsø, Norway.
authors.forename: Jonas
authors.initials: J
authors.lastname: Jusélius
authors.forename: Dage
authors.initials: D
authors.lastname: Sundholm
mesh_terms: D003627:Data Interpretation, Statistical; D008956:Models, Chemical; D055672:Static Electricity