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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Computational Tools for Electrostatics

Workshop on Ion Channels, Wed, 10 Oct, 2007

Speaker: Matthew Knepley

Abstract

Electrostatics provides the basis for interaction at the biologic level and underpins all current models of channel
activity. We will examine the computational structures inherent in modeling and solution of electrostatic problems
arising in channels. We will treat the both the background field, with realistic channel boundary conditions and
variable dielectric material properties, as well as consistent models for the interaction of free charged particles with
this field. The particles themselves may have differing dielectric properties. Several models for particle coupling will
be examined.

We wil introduce the PETSc computational framework (http://www.mcs.anl.gov/petsc), a collection of tools for
solving PDE such as the coupled Poisson-Newton system above. PETSc incorporates support for linear and nonlinear
algebraic solvers, many popular preconditioners including algebraic and geometric multigrid, structured and unstructured
meshes, as well as finite element and finite difference modeling. The solution of several representative channel
problems will be demonstrated.

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