The discretization of time-dependent wave propagation is plagued with dispersion
in which the wavefield is perceived to travel with an erroneous velocity. To remediate
the problem, simulations are run on dense and computationally expensive grids
yielding plausible approximate solutions. This work introduces an error analysis tool
which can be used to obtain optimal simulation parameters that account for mesh
size, orders of spatial and temporal discretizations, angles of propagation, temporal
stability conditions (usually referred to as CFL conditions), and time of propagation.
The classical criteria of 10-15 nodes per wavelength for second-order finite differences,
and 4-5 nodes per wavelength for fourth-order spectral elements are shown to be unrealistic
and overly-optimistic simulation parameters for different propagation times.
This work analyzes finite differences, spectral elements, optimally-blended spectral
elements, and isogeometric analysis.
|Date of Award||Jul 2012|
|Original language||English (US)|
- Physical Sciences and Engineering
|Supervisor||Victor Calo (Supervisor)|
- Finite Elements
- Wave Propagation
- Wave Equation
- Spectral Elements
- Isogeometric Analysis