The Principal Investigator proposes to carry out an interdisciplinary comprehensive research program combining the development, analysis and optimization of a new class of numerical methods, with their application to problems in seismology and electromagnetics. The novel methods hybridizes arbitrary-order Hermite approximations with arbitrary-order discontinuous Galerkin methods. The combination of these two methods will result in a new class of hybrid methods able to handle complex geometries and with unprecedented computational efficiency through large time steps and high-resolution. The methods have very large computation to communication ratio and are well suited for implementation on current and emerging supercomputer systems, enabling the solution of complex, multiple-scale evolutionary systems. The proposed unified analysis of discontinuous Galerkin methods and Hermite methods will require new tools and theories to be developed and will lead to a new theoretical framework for the analysis of hybrid methods. The proposal will consider methods for both first and second order formulations of the governing equations of elasticity and electromagnetics.
The research will have broader impacts in technology and science, as well as in the training of the next generation of computational scientists. As recent events in Japan have shown, earthquakes are a societal problem throughout the world. To better mitigate seismic hazard, effective prevention and prediction is needed. Careful assessment of seismic hazards through accurate computational predictions can lead to appropriate building codes. This can be of enormous impact for human life and societal welfare in the case of a large seismic event in a densely populated area as the greater Los Angeles or the San Francisco bay. The broader impacts of the proposed activities also include education. The project will involve graduate students who will gain experience in state-of-the-art computational science. The research will be performed at the University of New Mexico, a Hispanic serving institution that also serves a large body of native Americans, allowing active recruitment and education of students from underrepresented groups.
