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.
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.
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.
His major current project is the creation an new third-order accurate CFD method called the Active Flux method, with many original features, sponsored by NASA under the Revolutionary Computational Aerodynamics program. Linked with this is joint work with Chris Fidkowski on entropy-based mesh adaptation. Another current interest is the design of improved Lagrangian hydrocodes that avoid “mesh imprinting” by emphasis on symmetry properties of the discretization, including the preservation of discrete vorticity.
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.
Heath Hofmann is a Professor of Electrical Engineering and Computer Science – Electrical and Computer Engineering Division. Professor Hofmann’s computational research focuses on the modelling of electromechanical devices and systems. An area of emphasis is the development of computationally efficient electromagnetic and thermal models of rotating electric machines based upon finite element analysis (FEA). Specific projects include the development of parallelizable preconditioners for steady-state magnetoquasistatic FEA solvers, the application of model-order-reduction techniques to thermal and electromagnetic finite-element models, nonlinear modeling of magnetic materials, integrated FEA-circuit simulations, and the development of “scaling” techniques that allow the user to efficiently create a suite of electric machines with different performance characteristics from a single design.
Christiane Jablonowski is an Associate Professor in the Department of Climate and Space Sciences and Engineering. Her research is highly interdisciplinary and combines atmospheric science, applied mathematics, computational science and high-performance computing. Her research suggests new pathways to bridge the wide range of spatial scales between local, regional and global phenomena in climate models without the prohibitive computational costs of global high-resolution simulations. In particular, she advances variable-resolution and Adaptive Mesh Refinement (AMR) techniques for future-generation weather and climate models that are built upon a cubed-sphere computational mesh. Variable-resolution meshes enable climate modelers to focus the computational resources on features or regions of interest, and thereby allow an assessment of the many multi-scale interactions between, for example, tropical cyclones and the general circulation of the atmosphere.
Dr. Jablonowski organizes summer schools, dynamical core model intercomparison projects, teaches tutorials on parallel computing and climate modeling, develops cyber-infrastructure tools for the climate sciences, and has co-edited and co-authored a book on numerical methods for atmospheric models.
Ann Jeffers is an Associate Professor in the Department of Civil and Environmental Engineering. Her research seeks to use computational methods to study structural performance under fire hazards. Jeffers’ work has particularly focused on coupling a high-resolution CFD fire model to a low resolution structural model to study structural performance under natural fire effects. The coupled fire-structure simulation has necessitated the formulation of novel finite elements and algorithms to bridge the disparities between the fire and structural domains. She has also conducted research using probabilistic methods (i.e., Monte Carlo simulation and analytical reliability methods) to study the propagation of uncertainty and evaluate the reliability of structural systems threatened by fire.