Multipliers‐free dual‐primal domain decomposition methods for nonsymmetric matrices and their numerical testing

Abstract The most commonly used nonoverlapping domain decomposition algorithms, such as the FETI‐DP and BDDC, require the introduction of discontinuous vector spaces. Most of the works on such methods are based on approaches that originated in Lagrange multipliers formulations. Using a theory of partial differential equations formulated in discontinuous piecewise‐defined functions, introduced and developed by Herrera and his collaborators through a long time span, recently the authors have developed an approach to domain decomposition methods in which general problems with prescribed jumps are treated at the discrete level. This yields an elegant and general direct framework that permits analyzing the problems in greater detail. The algorithms derived using it have properties similar to those of well‐established methods such as FETI‐DP, but, in our experience, they are easier to implement. Also, they yield explicit matrix formulas that unify the different methods. Furthermore, this multipliers‐free framework has permitted us to extend such formulas to make them applicable to nonsymmetric matrices. The extension of the unifying matrix formulas to nonsymmetric matrices is the subject matter of the present article. A conspicuous result is that in numerical experiments in 2 D and 3 D , the MF‐DP algorithms for nonsymmetric matrices exhibit an efficiency of the same order as state‐of‐the‐art algorithms for symmetric matrices, such as BDDC, FETI‐DP, and MF‐DP.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1262‐1289, 2011