Now showing items 1-5 of 5
A reduced basis method for molecular dynamics simulation
In this dissertation, we develop a method for molecular simulation based on principal component analysis (PCA) of a molecular dynamics trajectory and least squares approximation of a potential energy function. Molecular ...
Vector basis function solution of Maxwell's equations
A general technique for solving Maxwell's equations exactly, based on expansion of the solution in a complete set of vector basis functions has been developed. These vector eigenfunctions are derived from the complete set ...
Preconditioning the integral formulation of the Helmholtz equation via deflation
In this thesis we propose methods for preconditioning Krylov subspace methods for solving the integral equation formulation of the Helmholtz partial differential equation for modeling scattered waves. An advantage of using ...
Global analysis of linearized inversion for the acoustic wave equation
To predict the location of natural resources and reduce the cost of exploration, geophysicists rely on various techniques to map the internal structure of the earth. One common mapping method probes the earth's interior ...
Geometrical optics for quasi-P waves: Theories and numerical methods
The quasi-P wave in anisotropic solids is of practical importance in obtaining maximal imaging resolution in seismic exploration. The geometrical optics term in the asymptotic expansion for the wave characterizes the high ...