Master of Science (MS)
First Committee Member
C. S. Chen
Number of Pages
In recent years, the method of fundamental solutions (MFS) has emerged as a novel meshless method in the scientific computing community. In the past, the MFS was essentially restricted to solving homogeneous elliptic equations. Recently, the MFS has gradually extended to solving various types of elliptic and time-dependent problems through the uses of radial basis functions (RBFs); In this thesis, we focus on solving wave equations through the MFS. Currently, there are two major approaches to solve the wave equation: (i) elimination of the time dependence by using the Laplace transform and (ii) discretization in time to approximate the time derivative. We propose to reduce the given wave equations to a series of inhomogeneous modified Helmholtz equations. The solution can then be split into evaluating both homogeneous and particular solutions. To evaluate the homogeneous solution, the MFS is adopted. Furthermore, a closed form particular solution is required for the proposed method. Intensive numerical tests are performed to compare the advantages and disadvantages of these two approaches.
Equations; Fundamental; Method; Solutions; Solving; Wave
Mathematics; Computer science
University of Nevada, Las Vegas
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Rivera, Lourdes Jeanette, "The method of fundamental solutions for solving wave equations" (2005). UNLV Retrospective Theses & Dissertations. 1850.