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Krzysztof Fidkowski

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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.

Results of adaptive simulations of a three-dimensional wing undergoing flapping motion in viscous flow. The target output of interest is the lift at the end of the simulation. Tailored meshes are created by increasing the approximation order on selected elements identified by an output-sensitivity error estimate. The resulting output converges much faster in terms of total degrees of freedom used when compared to other adaptive methods, including residual-based adaptation and uniform order refinement.

Results of adaptive simulations of a three-dimensional wing undergoing flapping motion in viscous flow. The target output of interest is the lift at the end of the simulation. Tailored meshes are created by increasing the approximation order on selected elements identified by an output-sensitivity error estimate. The resulting output converges much faster in terms of total degrees of freedom used when compared to other adaptive methods, including residual-based adaptation and uniform order refinement.

Vikram Gavini

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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.

Hierarchy of triangulations that form the basis of a coarse-graining methods (quasi-continuum reduction) for conducting electronic structure calculations at macroscopic scales.

Hierarchy of triangulations that form the basis of a coarse-graining methods (quasi-continuum reduction) for conducting electronic structure calculations at macroscopic scales.