Colloquium: Prof. Christopher Cooper, Universidad Técnica Federico Santa María
Prof. Christopher Cooper is visiting UNM for two days, coming from the Department of Mechanical Engineering, Universidad Técnica Federico Santa María.
Title: "A fast and accurate solution of the Poisson-Boltzmann equation with boundary elements"
The Poisson-Botlzmann equation is widely used to model the electrostatics of molecular solvation, in particular, to represent the salty water that surrounds a solute in biological settings. This is usually coupled with the Poisson equation, which governs inside the solute, and both equations are coupled on the molecular surface. We formulate the system of partial differential equations as integrals along the solute-solvent interface, and solve with a boundary element method (BEM) implemented in the PyGBe code. Compared to volumetric-based counterparts, a BEM offers an accurate representation of the molecular surface, leading to a more exact numerical solution. In contrast, the resulting matrices are dense, making it a O(N^2) method.
In this talk, we will look at techniques for an efficient solution of this BEM system. In particular, we will focus on two things: (1) the acceleration through a GPU-based treecode to decrease the scaling to O(N log N), and (2) the use of a posteriori error estimation techniques to build efficient meshes on the molecular surface, without sacrificing accuracy.
Contact Name: Prof. Chaudhry