A Priori Error-Controlled Simulations of Electromagnetic Phenomena for HPC

The project will remove a key difficulty that currently hampers many existing methods for computing unsteady electromagnetic waves in unbounded regions. The accuracy and/or stability of the simulations may deteriorate over long times due to the treatment of the outer boundaries via artificial boundary conditions. We propose to develop a universal algorithm and software that will correct this problem by employing the Huygens"principle and quasi-lacunae in the solutions of Maxwell"s equations. The algorithm will provide a temporally uniform guaranteed error bound (no deterioration at all), and the software will enable robust electromagnetic simulations in a high-performance computing environment. The methodology will apply to any geometry, any numerical scheme and any treatment of outer boundaries. It will eliminate the long-time deterioration regardless of both its origin and the way it manifests itself. Dr. Tsynkov of NCSU, who invented this method and is referenced in the Solicitation, is the Academic partner on the project. Phase I includes development of an innovative numerical methodology for high fidelity error-controlled modeling of a broad variety of electromagnetic and other wave-dominated phenomena. Solutions to test problems will be verified against analytical and accurate numerical benchmarks, to demonstrate the feasibility of the proposed approach. In Phase II our innovative algorithms will be implemented as robust commercial software tools in a standalone computational module that can be used to fix existing numerical schemes, along with the treatment of the outer boundaries, in computational electromagnetic codes.