This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The use of the basic principle of conservation has led to accurate and reliable mathematical models of the physical world. Such models, known as conservation laws, together with the related models such as Hamilton-Jacobi equations, display rich features in solutions and therefore continue to challenge the computational scientists. The primary objective of this CAREER proposal is to make several important steps towards the development and applications of high order accurate methods for solving these nonlinear equations. Discontinuous Galerkin methods will constitute the core methodology of this effort, this is due to their great flexibilities and capabilities in accurately and reliably simulating complicated problems. The project will comprehensively cover the algorithm design, analysis, implementation and applications.
The success of the proposed research will have direct impact on the efficient and robust modeling of problems in areas as diverse as optimal control, image processing, computer vision, astrophysics, space physics and energy physics. The resulting ideas and methodologies will bring new components to reliably simulate nonlinear problems and complex systems arising in science, physics and engineering. Besides training graduate and undergraduate students in conducting research in computational science, mentoring women students in mathematics, the proposed educational and academic activities will also enhance interaction and collaborations among regional research groups.
