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… (More)

Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to “lag” the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for… (More)

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… (More)

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)… (More)

We consider the approximation of functions that are localized in space. We show that it is possible to define meshes to approximate such functions with the property that the number of vertices grows… (More)

November 2007 in Stockholm, Sweden with Nuruddin Farah, Somali Novelist, Roland Marchal, Senior Research Fellow at the Centre d’Études et de Recherches Internationales, Paris, Asha Hagi, member of… (More)

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… (More)

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key… (More)