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.
Most of his research and teaching involves parallel computing of some form: design of scalable algorithms and data structures; applications to numerous scientific problems such as a large multidisciplinary team modeling space weather or a small interdisciplinary group doing imputation on datasets of social preferences; and performance analysis, both experimental and analytical. These projects have used a variety of computer architectures, ranging from tens to hundreds of thousands of cores. He also works on algorithms for abstract fine-grain parallel computer models motivated by concerns such as time/number-of-processors/peak-power tradeoffs and the constraints imposed by the fact that computation is done in 2- or 3-dimensional space. Further, he develops serial algorithms for optimizing adaptive sampling problems such as adaptive clinical trials, algorithms for isotonic regression, and various other computer science problems.
Dr. Toth works on algorithm and code development for space and plasma physics simulations. He has a leading role in the development of the Space Weather Modeling Framework (SWMF) that can couple and execute about a dozen different space physics models modeling domains from the surface of the Sun to the upper atmosphere of the Earth. He is one of the main developers of the BATS-R-US code, a multi-physics and multi-application magnetohydrodynamics code using block-adaptive grids. He is collaborating with many colleagues and students using the SWMF and BATSRUS for a wide range of applications: solar corona, coronal mass ejections, magnetic storms, comets, moons (Titan, Enceladus), planetary magnetospheres (Earth, Venus, Mars, Jupiter, Saturn), interaction of moons with their plasma environment (Titan, Enceladus), interaction of comets with the solar wind, outer heliosphere interaction with the inter-stellar material, etc. The SWMF is used by the Community Coordinated Modeling Center (CCMC) at NASA Goddard for research as well as real-time forecasting of space weather. Dr. Toth was also the software architect for the Center for Radiative Shock Hydrodynamics (CRASH). This DoE funded center worked on modeling radiative shocks created by high energy lasers and the uncertainty quantification of the model results. He has designed and implemented of the Versatile Advection Code, a general purpose publicly available hydrodynamics and MHD code. VAC has been used by hundreds of researchers around the world to simulate various hydrodynamic and MHD problems.
His research interests focus on understanding the physical processes controlling energetic charged particle motion in planetary magnetospheres, including Earth. He writes and uses space plasma physics numerical models, especially kinetic modeling that resolves velocity space distributions but also large-scale magnetohydrodynamic models. Prof. Liemohn is especially interested in the nonlinear coupling within planetary magnetospheres during strong solar wind driving intervals (i.e., system-level feedback during space storms).