My research focus is numerical methods for wave propagation in a variety of situations and media. I am currently working with Professor Michael Motley on a numerical wave tank model to support future experiments designed to estimate tsunami loads on bridges and help develop mitigation strategies.
My doctoral work was on wave propagation in poroelastic materials; I worked with Professor Randall J. LeVeque of the University of Washington and Professor Yvonne Ou of the University of Delaware to develop a simulation code in LeVeque's Clawpack framework suitable for modeling poroelastic, elastic, and acoustic wave propagation in biological and geophysical settings. Modeling applications include ultrasound and extracorporeal shock wave therapy (ESWT) applied to bone, and propagation of seismic waves in oil- or water-bearing rock formations.
|3D demonstration problem. This is a test case designed to exercise as much as possible of the functionality of the new parallel three-dimensional poroelastic-fluid simulation code. It features an uneven surface modeled using a mapped grid, a fluid-poroelastic interface, and an orthotropic material whose principal directions are different at every point.|
|Cylindrical scatterer. This is a verification case designed to test that the code correctly handles non-rectilinear mapped grids and interfaces between fluids and poroelastic materials. The test case used is a cylinder of poroelastic material in a fluid bath, struck by acoustic waves. The surface of the cylinder is completely permeable to the outside fluid. The problem is time-harmonic, and the numerical solution is compared against an analytical solution obtained by Professor Yvonne Ou at the University of Delaware.|
|Simplfied femur model. This shows an adult human femur (modeled as a cylinder of spongy cancellous bone, surrouned by a shell of hard cortical bone) in a water bath, struck by an acoustic pulse with a Gaussian profile. The outer surface of the bone is modeled as impermeable.|
|Point source results for homogeneous anisotropic media. These test cases were used to check the code against results from previous literature for anisotropic media.|
|Point source results in a bed of shale overlying a bed of sandstone. This case follows the discontinuous Galerkin work of de la Puente et al. (2008). It showcases the use of adaptive mesh refinement, and the interconversion between wave families at a material discontinuity.|