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

研究者将研究一种构造最优速度有限元解的新方法的潜力。对于一类有界单调椭圆型系统，该方法求解离散商空间中的有限元模型，其复杂度主要取决于微分有限元算子的核，并与系统中的未知数数成线性比例。研究者将证明该方法有许多优点，并寻求将其扩展到更具挑战性的问题，如对流主导的扩散。这项提议的研究是高性能科学计算的核心，在过去的几十年里，它一再被美国国家科学基金会确定为一项关键任务。2003年，美国能源部公布了一份名为《大规模模拟的科学案例》的两卷报告，该报告由300多名美国领先的计算科学家直接编写，其中发现大规模模拟的有效求解算法与建造超级计算机一样重要。调查人员直接回应电话，坚定地承诺推进这项任务。

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.