FETI Algorithms for Mortar Methods

研究人员Dan Stefanica将有限元撕裂和互连（FETI）算法扩展到砂浆方法，从而利用砂浆元素固有的灵活性。 他建立了由此产生的算法保持一致元素的FETI方法的收敛性。 这与低阶砂浆有限元的FETI算法的大量数值试验结果一致。 他检查是否条件数估计获得的FETI算法的迫击炮是尖锐的。 他通过为这些算法提供数值和理论收敛性分析，将FETI方法扩展到谱方法和砂浆谱元素。 最后，他设计了双-原始FETI算法的几何符合和几何几何martort方法。在这个项目中分析的算法是区域分解方法，这是强大的，快速的，易于并行化的偏微分方程的数值求解方法所产生的大量的实际应用的大家庭的一部分。 研究人员夫妇的这些方法之一，FETI方法，与一个通用的离散化的方程，称为砂浆方法。 因此，他能够解决非常复杂的几何问题，同时将大部分计算工作集中在解决问题的关键部分。 FETI方法已经在大范围应用的大型并行代码中实现。 本计画所发展之改良，对于航空设计、计算力学及流体流动等问题之应用，将具有重要意义。

The investigator, Dan Stefanica, extends the Finite Element Tearing and Interconnecting (FETI) algorithms to mortar methods, thus taking advantage of the inherent flexibility of the mortar elements. He establishes that the resulting algorithms preserve the convergence properties of the FETI methods for conforming elements. This agrees with extensive numerical experiments for FETI algorithms for low order mortar finite elements. He checks whether the condition number estimates obtained for the FETI algorithms for mortars are sharp. He extends the FETI method to spectral methods and mortar spectral elements, by providing numerical and theoretical convergence analysis for these algorithms. Finally, he designs Dual--Primal FETI algorithms for both geometrically conforming and geometrically nonconforming mortar methods. The algorithms analyzed in this project are part of the larger family of domain decomposition methods, which are powerful, fast, and easily parallelizable methods for the numerical solution of partial differential equations arising from a large spectrum of practical applications. The investigator couples one of these methods, the FETI method, with a versatile discretization of the equations, called the mortar method. Thus, he is able to solve problems with very complicated geometry while concentrating most of the computational effort on resolving the critical parts of the problem. The FETI method has already been implemented in huge parallel codes for a large spectrum of applications. Improvements in it developed by this project will be important for such applications as aerospace design, computational mechanics and fluid flow problems.