Applied Math Seminar: Using spacetime tents to solve hyperbolic systems

Seminar | January 24 | 4-5 p.m. | 736 Evans Hall

 Jay Gopalakrishnan, Portland State University

 Department of Mathematics

(Note the special location) A spacetime simulation region can be subdivided into tent-shaped subregions. Tents appear to be natural for solving hyperbolic equations. Indeed, one can ensure causality by constraining the height of the tent pole. More precisely, the domain of dependence of all points within the tent can be guaranteed to be contained within the tent, by constraining the tent pole height. We consider techniques to advance the numerical solution of a hyperbolic problem by progressively meshing a spacetime domain by tent shaped objects. Such tent pitching schemes have the ability to naturally advance in time by different amounts at different spatial locations. One obtains spacetime discontinuous Galerkin (SDG) schemes - extensively studied by many authors - when the hyperbolic system on the tent is discretized in spacetime. We pursue another alternative by mapping each tent to a spacetime cylinder. These maps transform tents into domains where space and time are separated, thus allowing standard methods to be used within tents. Several open mathematical and computational issues surrounding these methods will be touched upon.

Reference: J. Gopalakrishnan, J. Schlberl, and C. Wintersteiger. "Mapped tent pitching schemes for hyperbolic systems." SIAM J Sci Comp, 39:6, p.B1043-B1063, 2017.