Physical Sciences and Mathematics Commons^™

Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton

Doctoral Dissertations

This dissertation consists of four integral parts with a unified objective of developing efficient numerical methods for high frequency time-harmonic wave equations defined on both homogeneous and random media. The first part investigates the generalized weak coercivity of the acoustic Helmholtz, elastic Helmholtz, and time-harmonic Maxwell wave operators. We prove that such a weak coercivity holds for these wave operators on a class of more general domains called generalized star-shape domains. As a by-product, solution estimates for the corresponding Helmholtz-type problems are obtained.

The second part of the dissertation develops an absolutely stable (i.e. stable in all mesh regimes) interior …

A Radial Basis Function Partition Of Unity Method For Transport On The Sphere, Kevin Aiton

Boise State University Theses and Dissertations

The transport phenomena dominates geophysical fluid motions on all scales making the numerical solution of the transport problem fundamentally important for the overall accuracy of any fluid solver. In this thesis, we describe a new high-order, computationally efficient method for numerically solving the transport equation on the sphere. This method combines radial basis functions (RBFs) and a partition of unity method (PUM). The method is mesh-free, allowing near optimal discretization of the surface of the sphere, and is free of any coordinate singularities. The basic idea of the method is to start with a set of nodes that are quasi-uniformly …