This research builds a unified computational framework for scalable and high efficiency solution of elliptic partial differential equations. The investigators develop a novel high-order multiscale multigrid computation methodology, which combines high accuracy computation and fast computing methods in a seamless way. This research work may impact many computational science and engineering and industry modeling and simulation applications. As U.S. high-tech industry moves from experiment-based design and development to computer-assisted design and development, higher performance numerical methods and faster computer simulation techniques will benefit U.S. industry by enabling design and development engineers to conduct quick verification to test their new ideas on computers, before committing to expensive experiments. These technologies are essential for the U.S. industry to maintain its leadership position in the competitive world market. Graduate students, including members from underrepresented groups, are trained to become the next generation researchers and educators with solid scientific computing skills.
The technique simultaneously advances the numerical solution of partial differential equations in two fronts. One is to compute high accuracy solution by using high-order discretization methods, another is to compute the discrete solution in a minimum amount of computer time by using the fastest sparse linear system solvers. This unified framework advances the two fronts collectively by fusing the ideas and advantages of multiscale discretization and multigrid computations, to achieve the ultimate goal of computing accurate numerical solution at the minimum computer costs. It is the convergence of years of research work by many researchers in several different areas. This computational framework possesses high accuracy, high speed, high scalability, and delivers optimal efficiency for computing the numerical solution of elliptic partial differential equations.
