Domain decomposition methods : algorithms and theory

By Andrea Toselli, Olof B. Widlund. 2005

2,552 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/87177b7c529056c68a6fa7933c9aa9381d5460f4

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Citations in the corpus

Multigrid for an HDG method (2013, background): “Examples can be found in (Toselli & Widlund, 2005) and (Bramble, 1993).”
Recent computational developments in Krylov subspace methods for linear systems (2007, background): “[13, 57, 261, 281, 326, 348] and references therein.”
Fusion frames and distributed processing (2006, unknown): “Some approaches such as the domain decomposition method [29] also use coherent combinations.”
BOUNDARY CONDITIONS IN APPROXIMATE COMMUTATOR PRECONDITIONERS FOR THE NAVIER-STOKES EQUATIONS ∗ (2009, unknown): “1 (page 329) of [15] (see also the references therein), Robin conditions are discussed in terms of domain decomposition and how they enhance coercivity.”
Lagrangian formulation of domain decomposition methods: A unified theory (2006, methodology): “Beyond the possible algorithms well suited for parallel computers with distributed memory, the domain decomposition methods [42,39,45] are very efficient.”
Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case (2007, methodology): “For symmetric DG approximations, following the lines of the classical theory for Schwarz methods [43], we prove that the condition number of the preconditioned systems is of the order O(H/h) when TH and Th are quasiuniform (cf.”
Highly scalable parallel domain decomposition methods with an application to biomechanics (2010, methodology): “1, and, e.g., Toselli and Widlund [51, Chap.”
Total FETI—an easier implementable variant of the FETI method for numerical solution of elliptic PDE (2006, methodology): “in [10].”
Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems (2005, methodology): “Our domain decomposition method for the solution of (1.1), (1.2) generalizes the Neumann-Neumann domain decomposition method, which is well known for the solution of single PDEs (see, e.g., the books [25, 29, 30 ]) to the optimization context.”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “Within this paper, the domain decomposition methods (DDMs) are employed for the solution of BVPs in multiple domains, see for instance [14].”
Non-Conformal Domain Decomposition Method With Mixed True Second Order Transmission Condition for Solving Large Finite Antenna Arrays (2011, methodology): “Domain decomposition methods (DDMs) [ 3 ]‐[7] have been employed as effective preconditioners to improve upon the vector finite element methods [2] for much larger electrical-size EM problems.”
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers (2009, methodology): “One can observe that the preconditioner described above has the matrix form of a primal Neumann-Neumann type of substructuring preconditioner [24] but applied to Lagrange multiplier degrees of freedom.”