Peter Brune

Argonne National Laboratory | ANL · Division of Mathematics and Computer Science

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solutio...

We discuss fast and accurate evaluation of local averages on GPGPU. This work was motivated by the need to calculate reference fluid densities in the classical density functional theory (DFT) of electrolytes proposed in Gillespie et al. (2002). In Knepley et al. (2010) we developed efficient algorithms for the minimization of three-dimensional DFT...

In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact their eigenfunctions are th...

The nonlocal continuum dielectric model is an important extension of the classical Poisson dielectric model, but it is very expensive to be solved in general. In this paper, we prove that the solution of one commonly used nonlocal continuum dielectric model of water can be split as a sum of two functions, and these two functions are simply the solu...

Continuum electrostatic theory based on the Poisson equation has proven to be a surprisingly effective simple model for understanding protein function, but it has not enjoyed equal success in every application. In particular, calculations of protein pKa shifts have seemed to require substantially different treatment than other calculations. Many gr...

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We introduce a simplification of a general topologically-motivated mesh coarsening algorithm for use in creating...