Ignacio Tomas
Texas Tech University, TX·Mathematics & Statistics
Electric charge moving through devices like high-frequency semiconductors, microwave sources and high-voltage pulsed-power systems behaves partly like a fluid. Engineers depend on computer simulations to design these technologies, but simulations of fast-changing charge flow can break down.
- Fields
Mathematics & Statistics
Engineering
Physics
- Topics
numerical analysis
scientific computing
Euler-Maxwell equations
- Grants
- 1 known grant, through Aug 2027
What they work on
- Develop semi-implicit time-stepping schemes for the Euler-Maxwell and Euler-Poisson fluid models of charge transport that keep density positive and energy stable, even when fast plasma oscillations are present.
- Create new formulations and numerical solvers for Maxwell's equations, the laws of electromagnetism, that couple robustly to fluid models of moving electrons.
- Build the mathematical theory for graph-based solvers of nonlinear hyperbolic systems, equations that describe waves and shocks, with guarantees such as a minimum principle for specific entropy.
- Implement the new methods for high-performance computing in the deal.II finite-element library and apply them to phenomena such as the Diocotron instability.
More about the research
They can produce impossible results such as negative densities, or become numerically unstable. This project aims to build simulation methods that are mathematically guaranteed to stay reliable.
Why it matters
Better simulations of high-frequency charge transport could help engineers design new semiconductor devices, microwave sources and high-voltage pulsed-power equipment, including directed energy systems. Methods guaranteed not to produce unphysical results or blow up numerically would make these predictions more trustworthy. That could reduce reliance on costly trial-and-error in device development.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Matthias Maier
Texas A&M University-College Station, TX·Mathematics & Statistics·Early-career
Develop and analyze numerical methods for time-harmonic (single-frequency) simulations of non-local conductivity, where a material's electrical response depends on nearby conditions, in nanoscale optical geometries.
Benjamin Seibold
Temple University, PA·Mathematics & Statistics
Construct explicit and implicit-explicit Runge-Kutta time-stepping methods that satisfy weak stage order, an algebraic condition on the method's coefficients that prevents the loss of accuracy known as order reduction, and build the supporting algebraic theory.
Yiwei Wang
University of California-Riverside, CA·Mathematics & Statistics
Develop high-order variational Lagrangian schemes, which track moving parcels of material, for generalized diffusion models, built directly from the energy and dissipation description of the fluid.
The school
Texas Tech University: 9 labs on PI Pages, $257M a year on research, 415 research doctorates a year.
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