I conduct scientific modeling by mathematical and numerical analysis with research focused on high-performance methods
for solving partial differential equations (PDEs) in the study of natural phenomena.
Much of my work is motivated by the fundamental desire to construct methodologies that faithfully preserve the underlying
physics of computational models, and seeks to identify interdisciplinary problems in science and engineering
that can provide mutual validation of both numerical simulation and experiment. Current interests are centered on
- frequency-domain boundary element methods: fast multipole methods with applications to acoustic scattering, anisotropic mesh generation (Figure 1)
- time-domain Fourier continuation methods: linear elasticity with applications to NDT (Figure 2) and seismology/geophysics (Figure 3), arterial flow with applications to cardiac physiology (Figure 4)
- high-performance computing for both shared and distributed memory parallel clusters