Martins’ research is on algorithms for multidisciplinary design optimization (MDO) that can take advantage of high-fidelity simulations and high-performance parallel computing. He has been focusing on applying these algorithms to the design optimization of new aircraft configurations. In the design of an aircraft wing in particular, since it is flexible, it is crucial to consider the coupling of the aerodynamics and the structure. In addition, when performing design optimization, it is important to simultaneously account for the aerodynamic performance and the structural failure constraints. In the MDO Lab, Martins’ team has developed ways to perform design optimization based a Reynolds-averaged Navier-Stokes model for the aerodynamics that is tightly coupled to a detailed structural finite-element model. The optimization of the coupled system is done with a gradient-based algorithm, where the gradients of the coupled system are computed using a two-field adjoint system of equations. This enables the high-fidelity aerostructural design of aircraft configurations with respect to thousands of design variables.
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.
Fidkowski’s research interests lie in the development of robust, scalable, and adaptive solvers for computational fluid dynamics. Target applications include steady and unsteady convection dominated flows, such as those observed in external aerodynamics. Quantitative numerical error estimates for these problems are important for vehicle analysis and design; however they are challenging to obtain, especially for multi-dimensional simulations involving complex physical models running on parallel architectures. Fidkowski’s group is applying adjoint-based error estimation techniques to these problems, with the goal of generating tailored meshes for the prediction of selected outputs of interest. Research topics under investigation include improving effectivity of error estimates, applying error estimation to novel discretizations, combining error estimation with uncertainty quantification and optimization, and diversifying adaptation mechanics, especially for high-order unsteady simulations on deformable domains.
His research is in computational physics, specifically biophysics (tumor growth and cell mechanics) and materials physics (battery materials, structural alloys and semiconductor materials). In these areas Garikipati’s group focuses on developing mathematical and numerical models of phenomena that can be described by continuum analyses that translate to PDEs. Usually, these are nonlinear, and feature coupled physics, for example chemo-thermo-mechanics. Our numerical techniques are mesh-based variational methods such as the finite element method and its many variants. In some problems we make connections with fine-grained models, in which case we work with kinetic Monte Carlo, molecular dynamics or electronic structure calculations in some form. In the realm of analysis, we often examine the asymptotic limits of our mathematical models, and the consistency, stability and convergence of our numerical methods.
His research group aims to develop computational and mathematical techniques to address various aspects of materials behavior, which exhibit complexity and structure on varying length and time scales. The work draws ideas from quantum mechanics, statistical mechanics and homogenization theories to create multi-scale models from fundamental principles, which provide insight into the complex behavior of materials. Topics of research include developing multi-scale methods for density-functional theory (electronic structure) calculations at continuum scales, electronic structure studies on defects in materials, quasi-continuum method, analysis of approximation theories, numerical analysis, and quantum transport in materials.