This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The spacetime discontinuous Galerkin (SDG) method is a new computational technology whose novel mathematical framework leads to algorithms that have the potential for significant impact in a wide variety of application disciplines wherever high-resolution solutions to systems of partial and ordinary differential equations are required. The exploratory research program proposed here would demonstrate the feasibility of extending the SDG methodology to a general-purpose numerical framework for solving systems of PDEs of arbitrary type in up to 3D ×time. The technology will be based on unique adaptive spacetime meshing, building up on the classical discrete Hamiltonian dynamics theory to a true field theory. Project will also introduce a new multi-scale hyperbolic relaxation for approximating parabolic systems, and an hp-adaptive, causality-based approach to modeling conservation laws that requires no numerical stabilization beyond the basic SDG Galerkin projection.
