The investigator is studying connections between conventional finite element methods and the cutting edge discontinuous Galerkin method. Only recently has it been discovered that the differential operators discretized via these philosophically distinct methods have closely related eigenspectra. The investigator is synthesizing analytical and numerical tools from both fields to examine and improve the robustness of the latter method when used with highly non-conforming discretization resolution. In addition, the investigator and a graduate student are creating an object oriented library which allows non-experts to use combinations of these methods through a simple and intuitive interface.
As new techniques for computational simulation of physical phenomena are developed, it is extremely important to determine under what circumstances they perform at their best and in a predictable way. There has been significant interest in the recently developed discontinuous Galerkin simulation method, because it can solve large scale problems not readily attainable with existing methods. For example, these methods can potentially increase the accuracy, efficiency, and scope of modeling radar scattering from large complex aircraft. The investigator is studying how to predict when this new method will give physically reasonable solutions, for example in computing the noise generated by next generation aircraft. The end product of this investigation will be a set of guidelines on how and when to best use the methods. Furthermore, the investigator is developing a software library which will ease transfer of these high resolution methods by simplifying the process of rapid prototyping and testing of new critical core components for physics simulation tools.
