Record Details
The Variable Speed Wave Equation and Perfectly Matched Layers
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | The Variable Speed Wave Equation and Perfectly Matched Layers |
| Names |
Kim, Dojin
(creator) Finch, David V. (advisor) |
| Date Issued | 2015-06-04 (iso8601) |
| Note | Graduation date: 2016 |
| Abstract | A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain. We introduce a new formulation from regularizing the classical Un-Split PML of the acoustic wave equation and show the well-posedness and numerical efficiency. A PML is designed to absorb incident waves traveling perpendicular to the PML, but there is no effective absorption of waves traveling with large incident angles. We suggest one method to deal with this problem and show well-posedness of the system, and some numerical experiments. For the 1-d wave equation with a constant speed equipped a PML, stability and the exponential decay rate of energy has been proved, but the question for variable sound speed equation remained open. We show that the energy decays exponentially in the 1-d PML wave equation with variable sound speed. Most PML wave equations appear as a first-order hyperbolic system with as a zero-order perturbation. We introduce a general formulation and show well-posedness and stability of the system. Furthermore we develop a discontinuous Galerkin method and analyze both the semi-discrete and fully discretized system and provide a priori error estimations. |
| Genre | Thesis/Dissertation |
| Topic | Perfectly Matched Layers |
| Identifier | http://hdl.handle.net/1957/56308 |
