FETI Algorithms for Mortar Methods

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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.