The Electromagnetics and Acoustics Group (EAG) focuses on simulations of wave propagation problems, including acoustics, electromagnetics, elastodynamics and various coupled problems. Our simulations are based on two tools. The first one if the hp-adaptive finite and boundary element methods where both element size h and polynomial order p vary locally to capture solution singularities or boundary layers. Both parameters h and p are determined in a fully automatic mode driven by an adaptive strategy aiming at minimization of the energy norm of the discretization error, or error in a specific quantity of interest. The hp-adaptive strategy produces a sequence of grids delivering exponential convergence, enabling solution of challenging problems with large material contrasts and dynamic range. The theory and hp codes have been documented in a two-volume book on "Computing with hp-Adaptive Finite Elements," published by Chapman and Hall/CRS Press.
More recently, we have turned from the classical (Bubnov-)Galerkin method to the Discontinuous Petrov Galerkin (DPG) method proposed by Demkowicz and Gopalakrishnan in 2009. DPG computes on fly optimal test functions that automatically guarantee the discrete stability if the continuous problems is well posed.
Our past applications included simulations of electromagnetic and sonic logging tools, analysis of unwanted noise in streamers, computation of Radar Cross Sections for objects with sharp edges and vertices, and simulations of acoustic waves in the Human Head.
All of our current projects are based on the DPG technology. In context of wave propagation and vibrations, we work on:
1. Modeling of insulators in high density electric motors (with Aleta Wilder and Federico Fuentes),
2. High wave number acoustics and electromagnetics (with Socratis Petrides and Jay Gopalakrishan),
3. Modeling of optical amplifiers (with Jacob Grosek and Sriram Nagaraj).
Other projects include:
4. Application of DPG to linear and non-linear elasticity and non-Newtonian fluids in context of modeling cardiovascular systems (with Brendan Keith, Marek Behr, and Patric LeTallec),
5. Application of Polyhedral DPG method to nonlinear elasticity (with Ali Vaziriastaneh, Jaime Mora Paz, and Joe Bishop),