| Date: Friday, February 04, 2011
Title: Accurate and Efficient Interface Methods for Implicitly Solvated Biomolecular Simulation
Abstract: Poisson-Boltzmann (PB) equation based implicit solvent model can greatly reduce the dimension and computational cost in simulating solvated biomolecular systems by applying the mean field approximation in permittivities and capturing the mobile ions with Boltzmann distribution. However, solving PB equation suffers many numerical difficulties ranging from discontinuous permittivities and electrostatic field across the dielectric interface, boundary conditions at infinity, geometric irregularities, and charge singularities. Two interface methods are attempted to resolve these difficulties. One is the matched interface and boundary (MIB) method, a high order finite difference mashed method, which repeatedly uses interface jump conditions to capture the non-smoothness of solutions, adaptively applies high order local interpolation to track the geometric irregularities and analytically takes Green's function based decomposition to regularize the singularities of the source. By computing a series of benchmark tests, the MIB PB solver has been proved to be by far the most accurate Cartesian grid based PB solver. The second one is the treecode accelerated boundary integral (TABI) method, which adopts a well conditioned boundary integral equation to handle these difficulties while accelerates the Krylov subspace based iterative methods such as GMRES with treecode. This Cartesian coordinates treecode is an O(NlogN) scheme with properties of easy implementation, efficient memory usage, and straightforward parallelization. Benchmark testing results on Kirkwood sphere plus simulations of biomolecules in various sizes are provided to demonstrate the accuracy, efficiency and robustness of the present methods.
Speaker: Weihua Geng
Institution: University of Michigan
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