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

研究人员将研究一种构造速度最优的有限元解算器的新方法的潜力。对于一类有界单调椭圆型系统，该方法在离散商空间中求解有限元模型，其复杂性主要取决于所描述的有限元算子的核，且与系统中的未知数成线性关系。研究人员将证明该方法具有许多优点，并寻求将其扩展到更具挑战性的问题，如对流主导的扩散。拟议的研究驻留在高性能科学计算的核心，在过去几十年里一再被国家科学基金会确定为关键任务。2003年，美国能源部公布了一份题为《大规模模拟的基于科学的案例》的两卷本报告，这份报告由300多名全国领先的计算科学家直接参与编写，其中发现用于大规模模拟的高效求解器算法与建造超级计算机一样重要。研究人员直接响应号召，承诺推进这项任务。

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.