Browsing by Subject "Fast multipole method"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Fast numerical methods for high frequency wave scattering(2012-05) Tran, Khoa Dang; Engquist, Björn, 1945-; Ling, Hao; Ghattas, Omar; Tsai, Richard; Ying, LexingComputer simulation of wave propagation is an active research area as wave phenomena are prevalent in many applications. Examples include wireless communication, radar cross section, underwater acoustics, and seismology. For high frequency waves, this is a challenging multiscale problem, where the small scale is given by the wavelength while the large scale corresponds to the overall size of the computational domain. Research into wave equation modeling can be divided into two regimes: time domain and frequency domain. In each regime, there are two further popular research directions for the numerical simulation of the scattered wave. One relies on direct discretization of the wave equation as a hyperbolic partial differential equation in the full physical domain. The other direction aims at solving an equivalent integral equation on the surface of the scatterer. In this dissertation, we present three new techniques for the frequency domain, boundary integral equations.Item Speed and accuracy tradeoffs in molecular electrostatic computation(2009-12) Chen, Shun-Chuan, 1979-; Bajaj, Chandrajit; Arikan, Okan; Dhillon, Inderjit; Rossky, Peter; Ying, LexingIn this study, we consider electrostatics contributed from the molecules in the ionic solution. It plays a significant role in determining the binding affinity of molecules and drugs. We develop the overall framework of computing electrostatic properties for three-dimensional molecular structures, including potential, energy, and forces. These properties are derived from Poisson-Boltzmann equation, a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. In order to compute these properties, we derived new boundary integral equations and designed a boundary element algorithm based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. Meanwhile, a higher-order parametric formulation called algebraic spline model is used for accurate approximation of the unknown solution of the linearized Poisson-Boltzmann equation. Based on algebraic spline model, we represent the normal derivative of electrostatic potential by surrounding electrostatic potential. This representation guarantees the consistent relation between electrostatic potential and its normal derivative. In addition, accurate numerical solution and fast computation for electrostatic energy and forces are also discussed. In addition, we described our hierarchical modeling and parameter optimization of molecular structures. Based on this technique, we can control the scalability of molecular models for electrostatic computation. The numerical test and experimental results show that the proposed techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules.