SGER: A New Finite Element Solver Algorithm of Optimal Speed and Robustness

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The investigator will investigate the potential of a new method for constructing finite element solvers of optimal speed. For a class of bounded monotone elliptic systems, the method solves the finite element model in a discrete quotient space, whose complexity depends mainly on the kernel of the discritized finite element operator, and is linearly proportional to the number of unknowns in the system. The investigator will demonstrate that the method has many advantageous features, and seek for extending it to to more challenging problems such asconvection-dominated diffusion.The proposed research resides at the heart of high performance scientific computation, having repeatedly been identified as a critical mission by National Sciences Foundation over the last several decades. In 2003, the U.S. Department of Energy publicized a two-volume report titled "A Science-based Case for Large Scale Simulation", prepared withdirect input from more than 300 of the nation's leading computational scientists, in which discovering efficient solver algorithms for large scale simulation is recognized as important as building supper computers.The investigator directly answer to the call with a strong promise to advance that mission.