By S. Bertoluzza, F. Brezzi, L.D. Marini, G. Sangalli (auth.), Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen, Dirk Roose, Tamar Schlick, Ralf Kornhuber, Ronald Hoppe, Jacques Périaux, Olivier Pironneau, Olof Widlund, Jinchao Xu (eds.)
ISBN-10: 3540225234
ISBN-13: 9783540225232
Domain decomposition is an energetic, interdisciplinary study region that's dedicated to the improvement, research and implementation of coupling and decoupling options in arithmetic, computational technological know-how, engineering and undefined. a sequence of foreign meetings beginning in 1987 set the level for the presentation of many in the meantime classical effects on substructuring, block iterative equipment, parallel and disbursed excessive functionality computing and so on. This quantity includes a choice from the papers offered on the fifteenth foreign area Decomposition convention held in Berlin, Germany, July 17-25, 2003 via the world's major specialists within the box. Its certain concentration has been on numerical research, computational issues,complex heterogeneous difficulties, commercial difficulties, and software program development.
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Additional resources for Domain Decomposition Methods in Science and Engineering
Sample text
We can collect the previous results, together with the abstract error estimates of the previous section, in the following theorem. 16 S. Bertoluzza, F. D. Marini, and G. Sangalli Theorem 3. Assume that the assumptions on the decompositions TδΣ and Ths of Section 2 are satisfied, and assume that the spaces Φδ , Mhs and Vhs are defined as in (43), (44) and (18) with (45), respectively. Assume finally that (48) holds. Then we have |||uh − u||| ≤ C (|h|k + |δ|k )||u||k+1,Ω (51) The proof follows immediately from Theorem 1, the results of this section, and usual approximation estimates.
This preconditioner is mathematically optimal in the sense that it leads to the condition number estimate (3). 2. The lumped preconditioner which can be written as L−1 Ns W(s) B(s) r FIrr = s=1 0 0 (s)T W(s) . (s) Br 0 Kbb (18) This preconditioner is not mathematically optimal in the sense defined above; however, it decreases the cost of each iteration in comparison with the Dirichlet preconditioner often with a modest increase in the iteration count. The FETI-DPH Method 25 3 The FETI-DPH method (s) (s) (s) In the context of Eq.
6) This form has a readily computable (pseudo-) inverse given by the fast diagonalization method (FDM) of Lynch et al. [1964], Hybrid Schwarz-Multigrid Methods A−1 = (S ⊗ S ) e Ley Ley I ⊗ Λ + Λ⊗I Lex Lex 39 −1 (S T ⊗ S T ), (7) where S is the matrix of eigenvectors and Λ the matrix of eigenvalues satisfying AS = BSΛ and S T BS = I. The bracketed term in (7) is diagonal, and its pseudo-inverse is computed by inverting nonzero elements and retaining zeros elsewhere. For arbitrarily deformed elements, the discrete Laplacian cannot be expressed in the tensor-product form (6), and the FDM cannot be used.
Domain Decomposition Methods in Science and Engineering by S. Bertoluzza, F. Brezzi, L.D. Marini, G. Sangalli (auth.), Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen, Dirk Roose, Tamar Schlick, Ralf Kornhuber, Ronald Hoppe, Jacques Périaux, Olivier Pironneau, Olof Widlund, Jinchao Xu (eds.)
by Charles
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