Title: Spacetime Discontinuous Galerkin Methods: A New Model for the Dynamics of Materials

Speaker: Robert B. Haber, Department of Mechanical Science & Engineering Center for Process Simulation and Design Materials Computation Center, University of Illinois at Urbana-Champaign Urbana, Illinois 61801 USA

Date/Time: Monday, May 11, 2009, 11:00 am

Location: JCEL 1811

Brief Abstract: This talk surveys interdisciplinary research at the University of Illinois on spacetime discontinuous Galerkin (SDG) methods implemented on adaptive grids that are fully unstructured in both space and time. SDG technology can be advantageous in problems requiring high-resolution, dynamic solutions. It offers linear computational complexity in the number of spacetime elements, element-wise balance proper¬ties with respect to spacetime Riemann fluxes, arbitrarily high-order accuracy (for smooth solutions) on compact stencils, favorable intrinsic stability properties, and an asynchronous, scalable structure for parallel computation.

I will briefly review of SDG fundamentals, including a coordinate-free development of balance laws on ar¬bitrary spacetime control volumes using differential forms and an interleaved spacetime mesh generation and finite-element solution procedure. Applications to elastodynamic fracture and hyperbolic heat conduction demonstrate the effectiveness of the SDG methodology. The fracture application highlights the use of adap¬tive spacetime meshing to track solution-dependent crack growth and a two-scale, delayed-damage cohesive model. I will close with a new sharp-interface model for concurrent, atomistic-to-continuum (AtC) coupling in simulations of the dynamics of solids. Enforcing the standard balance laws and compatibility relations in the SDG framework, with due attention to the atomic-scale configuration, suffices to achieve reflection-free coupling without resorting to various heuristic devices, such as overlap regions and non-physical damping.

CSRI POC: Rich Lehoucq, (505) 845-8939