Jamie Bramwell, University of Texas at Austin
KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation
May 7-8, 2011
King Abdullah University of Science and Technology (KAUST)
Thuwal, Kingdom of Saudi Arabia
A Discontinuous Petrov-Galerkin Method for Elastic Wave Propagation
Authors: Jamie Bramwell, Leszek Demkowicz, Jay Gopalakrishnan, and Weifeng Qiu
In previous research, a Discontinuous Petrov-Galerkin (DPG) finite element method with optimal test functions for static linear elasticity was introduced. A key result was the proof of quasi-optimality of the method without the use of the exact sequence. This implies that both h and p convergence can occur without the use of element spaces which conform to an exact sequence. From this work, I will present an outline of the quasi-optimality proof as well as make comparisons between our methods and the mixed method of Arnold, Falk, and Winther.
Additionally, the two methods can be extended to time-harmonic elastic wave propagation problems. A key feature of the DPG method is the reduction of pollution error, and can therefore be used to solve problems with a large number of wavelengths. Due to this fact, I will present numerical results for elastic wave scattering problems with high wave numbers. Also, since the DPG method is equipped with an a priori error estimator, I will present results from various 'greedy' adaptive schemes.
The principal contribution of this research is a practical adaptive 2D time-harmonic elasticity finite element code with a priori error estimation that can be used for high wave number problems. A particular application where this method could be applied is large-scale seismic wave propagation. In this poster, I will present an overview of the theoretical DPG framework, the specic formulation for both static and time-harmonic elasticity, and the numerical results for both cases.
- J. Bramwell, L. Demkowicz, and W. Qiu. Solution of Dual-Mixed Elasticity Equations using Arnold-Falk-Winther Element and Discontinuous Petrov-Galerkin Method, a Comparison. Technical Report 10-23, The Institute for Computational Engineering and Sciences, The University of Texas at Austin, June 2010.
- J. Bramwell, L. Demkowicz, J. Gopalakrishnan, and W. Qiu. An hp DPG Method for Linear Elasticity with Symmetric Stresses, in preparation.