Maps & Tents

Friday, June 30, 2017 - 9:00am - 9:50am
Keller 3-180
Jay Gopalakrishnan (Portland State University)
Tent-shaped spacetime regions appear to be natural for solving hyperbolic equations. By constraining the height of the tent pole, one can ensure causality. The subject of this talk is a technique 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. Local time stepping without losing high order accuracy in space and time is thus possible.

Known methods of this type use spacetime discretizations within tents, thus yielding locally implicit schemes. We present a new twist using certain maps, that makes fully explicit schemes possible even while using unstructured tents. 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.

Collaborators: Peter Monk, Paulina Sepúlveda, Joachim Schöberl, Christoph Wintersteiger