Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems
Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to give a detailed and self-contained presentation of these methods, including the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed that have not been covered in any monograph yet: the coupling of finite and boundary elements within the tearing and interconnecting framework including exterior problems, and the case of highly varying (multiscale) coefficients not resolved by the subdomain partitioning. In this context, the book offers a detailed view to an active and up-to-date area of research.
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Algorithm all-floating formulation Assumption 2.54 BDDC boundary element boundary element method classical formulation coarse elements coarse triangulation coefficient Computational condition number bound Corollary corresponding deﬁne defined Deﬁnition denote Dirichlet boundary Dirichlet boundary conditions discrete DOFs Domain Decomposition Methods equation equivalent estimate eUad exterior FETI method FETI-DP FETI/BETI method finite element ﬁrst ﬁxed fulﬁlled function Furthermore global Hilbert space i.xh IBEM implies interface interior jump operator ker.B ker.S Lagrange multipliers let Assumption linear Lipschitz domain mesh parameter Meshfree Methods multiscale Neumann Neumann problem Neumann-Neumann node xh norm Note piecewise constant preconditioner primal nodal variables problem quasi-uniform range.P Remark saddle point Schur complement Sect shape regularity constants Sobolev spaces solution solvers space stiffness matrix subdomain subdomain edge subdomain facet subdomain vertex subregions subspace Theorem three dimensions triangulation vector