By Jan Mandel, Charbel Farhat, Xiao-Chuan Cai
This quantity includes the complaints of the 10th foreign convention on area Decomposition equipment, which excited by the most up-to-date advancements in practical functions in structural mechanics, structural dynamics, computational fluid dynamics, and warmth move. The court cases of those meetings have turn into general references within the box and comprise seminal papers in addition to the newest theoretical effects and studies on useful purposes. This quantity is split into 4 elements: the 1st half comprises invited papers (some of which survey advancements over the last decade), and the opposite components assemble fabric from minisymposia and contributed displays below 3 headings: Algorithms, thought, and purposes. The digital model is out there at no extra cost to dealers of the print quantity. entry directions are supplied within the ebook. there's additionally the choice to buy simply the digital model, additionally on hand at the AMS book place: merchandise code CONM/218.E.
Read or Download Domain Decomposition Methods 10: The Tenth International Conference on Domain Decomposition Methods, August 10-14, 1997, Boulder, Colorado, USA (Contemporary Mathematics 218) PDF
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Additional info for Domain Decomposition Methods 10: The Tenth International Conference on Domain Decomposition Methods, August 10-14, 1997, Boulder, Colorado, USA (Contemporary Mathematics 218)
Example text
Let I i denote the union of interfaces surrounding Di . The entire solution process would then consist of the following steps: Parallel Preprocessing: 1. Parallel computation of subdomain ADi Di matrix LU factors. 2. Parallel computation of Schur complement block entries associated with each subdomain Di ∆SI i = AI i Di A−1 Di Di ADi I i . (18) 3. Accumulation of the global Schur complement S matrix #subdomains S = AII − (19) ∆SI i . i=1 Solution: Step Step Step Step Step Step (1) (2) (3) (4) (5) (6) uDi = A−1 Di Di bDi vI i = AI i Di uDi #subdomains wI = bI − i=1 vI i −1 xI = S wI yDi = ADi I i xI i xDi = uDi − A−1 Di Di yDi (parallel) (parallel) (communication) (sequential, communication) (parallel) (parallel) This algorithm has several deficiencies.
Figures 8(a) and 8(b) show calculations performed with the present non-overlapping domain-decomposition preconditioner for diffusion and advection problems. These figures graph the number of global FGMRES iterations needed to solve the discretization matrix problem to 10−6 accuracy tolerance as a function of the number of subproblem iterations. In this example, all the subproblem iteration parameters have been set equal to each other (m1 = m2 = m3 ). The horizontal lines show poor scalability of single domain ILU-FGMRES on meshes containing 2500, 10000, and 40000 solution unknowns.
Bjorstad, and W. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, Cambridge University Press, 1996. 22. H. Stone, Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5 (1968), 530–558. 23. J. Xu, An introduction to multilevel methods, Lecture notes: VIIth EPSRC Numerical Analysis Summer School, 1997. ca Contemporary Contemporary Mathematics Mathematics Volume 218, 218, 1998 Volume B 0-8218-0988-1-03001-6 A Non-Overlapping Domain Decomposition Method for the Exterior Helmholtz Problem Armel de La Bourdonnaye, Charbel Farhat, Antonini Macedo, Fr´ed´eric Magoul`es, and Fran¸cois-Xavier Roux 1.