FETI and Neumann-Neumann iterative substructuring methods: Connections and new results

Klawonn, Axel; Widlund, Olof B.

doi:10.1002/1097-0312(200101)54:1<57::aid-cpa3>3.0.co;2-d

Cited by 168 publications

(182 citation statements)

References 27 publications

Supporting

Mentioning

179

Contrasting

Order By: Relevance

“…can be used for solving the interface problem (8). Thus, instead of working with the inverse of the sum of the two Schur complements, we use the sum of the inverses.…”

Section: A Neumann-neumann Methodsmentioning

confidence: 99%

See 1 more Smart Citation

FETI-DP, BDDC, and block Cholesky methods

Widlund

2006

Int. J. Numer. Meth. Engng

190

195

View full text Add to dashboard Cite

Two popular non-overlapping domain decomposition methods, the FETI-DP and BDDC algorithms, are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulations of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are the same. Results of numerical experiments also confirm this result.

show abstract

“…can be used for solving the interface problem (8). Thus, instead of working with the inverse of the sum of the two Schur complements, we use the sum of the inverses.…”

Section: A Neumann-neumann Methodsmentioning

confidence: 99%

“…This corresponds to the use of redundant Lagrange multipliers, see [8]. But we need not worry since the Lagrange multiplier λ is always restricted to range (B Γ ), which is orthogonal to the null space of B T Γ .…”

Section: Matrix Analysis Of Feti-dp and Bddcmentioning

confidence: 99%

FETI-DP, BDDC, and block Cholesky methods

Widlund

2006

Int. J. Numer. Meth. Engng

190

195

View full text Add to dashboard Cite

show abstract

“…is to notice that for s ≠ j, the following relation holds between modified and classical scaling operatorsÃ (s) [42]:…”

Section: Scaling Issuementioning

confidence: 99%

Substructured formulations of nonlinear structure problems - influence of the interface condition

Negrello

Gosselet

Rey

et al. 2016

Int. J. Numer. Meth. Engng

View full text Add to dashboard Cite

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is usally too expensive to be computed exactly in practice: an approximate version has to be sought, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

show abstract

“…From the results, we conclude that the performance of the algorithm is not too sensitive to the value of the coefficient of fricrion and the efficiency of our algorithm is comparable to solving of the linear problems. Approximation II reduces the size of the dual problem n d with relatively minor effect on the Mandel and Tezaur [1996], Klawonn and Widlund [2001]) and quadratic programming (see Dostál and Schöberl [2003], Dostál [2003]), it is possible to show that our algorithm for the problem with given friction is scalable.…”

Section: Numerical Experiments and Conclusionmentioning

confidence: 99%