Silas Alben is an Associate Professor in the Department of Mathematics, and the Director of the Applied & Interdisciplinary Mathematics program. He uses theoretical analysis, and develops numerical methods and models of problems arising from biology, especially biomechanics and engineering. Some of his group’s current applications are piezoelectric flags, flag fluttering in inviscid channel flow, snake locomotion and jet-propelled swimming.
Santiago Schnell’s lab combines chemical kinetics, molecular modeling, biochemical measurements and computational modeling to build a comprehensive understanding of proteostasis and protein forlding diseases. They also investigate other complex physiological systems comprising many interacting components, where modeling and theory may aid in the identification of the key mechanisms underlying the behavior of the system as a whole.
His research focuses on understanding the role of strong correction effects in many-body quantum systems. The objective is to discover novel quantum states/materials and to understand their exotic properties using theoretical/numerical methods (with emphasis on topological properties). In his research, numerical techniques are applied to resolve the fate of a quantum material (or a theoretical model) in the presence of multiple competing ground states and to provide quantitative guidance for further (experimental/theoretical) investigations.
Eric Michielssen is a Professor of Electrical Engineering and Computer Science – Electrical and Computer Engineering Division and Associate Vice President for Advanced Research Computing.
His research interests include all aspects of theoretical, applied, and computational electromagnetics, with emphasis on the development of fast (primarily) integral-equation-based techniques for analyzing electromagnetic phenomena. His group studies fast multipole methods for analyzing static and high frequency electronic and optical devices, fast direct solvers for scattering analysis, and butterfly algorithms for compressing matrices that arise in the integral equation solution of large-scale electromagnetic problems.
Furthermore, the group works on plane-wave-time-domain algorithms that extend fast multipole concepts to the time domain, and develop time-domain versions of pre-corrected FFT/adaptive integral methods. Collectively, these algorithms allow the integral equation analysis of time-harmonic and transient electromagnetic phenomena in large-scale linear and nonlinear surface scatterers, antennas, and circuits.
Recently, the group developed powerful Calderon multiplicative preconditioners for accelerating time domain integral equation solvers applied to the analysis of multiscale phenomena, and used the above analysis techniques to develop new closed-loop and multi-objective optimization tools for synthesizing electromagnetic devices, as well as to assist in uncertainty quantification studies relating to electromagnetic compatibility and bioelectromagnetic problems.
Dr. Maki works in the field of fluid mechanics, and his central focus is on developing algorithms for numerical computation of high-Reynolds number external flows that contain an air-water interface. Research interests include investigating free-surface hydrodynamics for analysis and design of high-performance naval craft and renewable-energy devices. Theoretical effort is focused on accurate description of the flow about marine vessels. Numerical research employs finite-volume and boundary element techniques to solve equations appropriate to govern the performance of ships maneuvering in waves, and energy devices and structures that operate in the ocean.
High power laser plasma interactions are interesting for applications such as the generation of energetic, directional electron, photon, ion and neutron beams or inertial fusion energy. Because of the strong electric and magnetic fields that lead to extremely far from equilibrium distributions, describing realistic high power laser interactions with plasma typically requires codes using a fully kinetic description. Professor Thomas’ research involves collisional plasma simulation using Vlasov-Fokker-Planck codes, including implicit methods using Krylov solvers for heat transport problems relating to inertial fusion energy. He is also interested in plasma simulation using particle-in-cell methods, including coupling the plasma code to very energetic photons using a Monte-Carlo method, for ultra intense short pulse laser interactions in radiation dominated regimes.
His research group develops fast and scalable algorithms for solving differential and integral equations on complex moving geometries. Application areas of current interest include large-scale simulations of blood flow through arbitrary confined geometries, electrohydrodynamics of soft particles and heat flow on time-varying domains.
Divakar Viswanath is a Professor in the Department of Mathematics. His research is at the interface of scientific computation and nonlinear dynamics. The incompressible Navier-Stokes equations are a major point of current interest. Turbulent dynamics is locally unstable and bounded in phase space. In such scenarios, dynamical systems theory predicts the existence of periodic solutions (modulo symmetries). Professor Viswanath has developed algorithms to extract periodic solutions and traveling waves from turbulent dynamics. One goal of current research is to derive, implement, and demonstrate algorithms that simulate turbulent flows at higher Reynolds numbers than is currently possible. It appears that this goal will be met shortly. Professor Viswanath has a general interest in foundational numerical analysis ranging from interpolation theory to the solution of differential equations.
Prof. Powell’s work focuses on algorithm development for fluid dynamics, aerodynamics and plasmadynamics, and the application of computational methods to problems in aerodynamics, aeroelasticicty, fluid dynamics and space environment/space weather.