Robert Krasny

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  A Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver for Electrostatics of Solvated Proteins
  Robert Krasny
  Electrostatic effects play an important role in determining protein structure and function. Here we present a treecode-accelerated boundary integral (TABI) solver for the electrostatic potential of a solvated protein described by the linear Poisson-Boltzmann equation. In this model the solvent is a continuum dielectric material with screening due to dissolved ions and the protein is a set of charged particles. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated by MSMS and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES and the matrix-vector product is carried out by a tree code which reduces the computational cost from $O(N^2)$ to $O(Nlog N)$, where $N$ is the number of faces in the triangulated molecular surface. We compare TABI results to those obtained using the finite-difference APBS code. The TABI solver exhibits good serial and parallel performance, with relatively simple implementation, efficient memory usage, and geometric adaptability. This is joint work with Weihua Geng (Southern Methodist University).