Convergence of a substructuring method with Lagrange multipliers
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The convergence of a substructuring iterative method with Lagrange multipliers is analyzed. This method was recently proposed by \textit{C. Farhat} and \textit{F.-X. Roux} [Int. J. Numer. Methods Eng. 32, No. 6, 1205-1227 (1991; Zbl 0758.65075)]. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, an asymptotic bound on the condition number is derived.
- University of Colorado Denver United States
Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Lagrange multipliers, convergence, Boundary value problems for second-order elliptic equations, finite element, preconditioning, Numerical computation of matrix norms, conditioning, scaling, substructuring iterative method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, condition number
Iterative numerical methods for linear systems, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Lagrange multipliers, convergence, Boundary value problems for second-order elliptic equations, finite element, preconditioning, Numerical computation of matrix norms, conditioning, scaling, substructuring iterative method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, condition number
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