Benjamin Seibold
Temple University, PA·Mathematics & Statistics
Simulating how something changes over time, such as water sloshing across a coastline or sound moving through air, usually means stepping a computer model forward in many small time increments. The accuracy of those steps is not guaranteed: well-established time-stepping schemes can quietly lose accuracy, a problem called order reduction, when applied to equations that have boundary conditions, hidden constraints or very fast and very slow behavior mixed together.
- Fields
Mathematics & Statistics
Engineering
Computer Science
- Topics
numerical analysis
time integration
Runge-Kutta methods
- Grants
- 1 known grant, through Jul 2027
What they work on
- 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.
- Develop multistep time integration methods for differential algebraic equations, where unknowns must satisfy constraints in addition to evolving in time.
- Prove time-stepping barrier theorems that establish the limits of attainable accuracy for stiff problems, which mix very fast and very slow dynamics.
- Apply the new methods to dispersive shallow water equations for storm surge and tsunamis, the incompressible Navier-Stokes equations, and advection-dominated hyperbolic conservation laws, and create pathways into community software.
More about the research
This project develops mathematical theory and new time-stepping methods that keep their expected accuracy on such problems while staying close enough in structure to existing methods that they can slot into software people already use.
Why it matters
Better time-stepping schemes make physics simulations more accurate at the same computational cost, which matters most where forecasts drive decisions. Improved shallow-water simulation could sharpen predictions of storm surge, tsunamis and hurricane-driven waves for coastal communities, and the methods are intended to reach practitioners through community software rather than staying in papers.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Ignacio Tomas
Texas Tech University, TX·Mathematics & Statistics
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.
Camillo De Lellis
Princeton University, NJ·Mathematics & Statistics
Prove the existence of Navier-Stokes solutions whose kinetic energy dissipation stays positive as viscosity goes to zero, without adding spurious oscillations to the initial data, giving rigorous examples of anomalous dissipation.
Theodore Drivas
Stony Brook University, NY·Mathematics & Statistics·Early-career
Analyze the long-time behavior of the two-dimensional Euler equations to explain how ideal fluids form lasting, hurricane-like vortices through vortex merging and mixing.
The school
Temple University: 22 labs on PI Pages, $315M a year on research, 238 research doctorates a year.
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