J. Douglas, Jr., and C.-S. Huang. An accelerated domain decomposition procedure based on Robin transmission conditions. To appear in BIT. Home/Search Document Details and Download
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An Agent-Based Approach to Building Multidisciplinary Problem.. - Drashansky (1996) (3 citations) (Correct)
....More details can be found in [MR95b, MR92b, Ric89] We do not discuss here the important mathematical questions of the convergence of the method, the behavior of the solution in crosspoints of the interfaces, etc. Some material concerning these questions can be found in [MR95b, RVY93, QV91, DH96, CHL91, CR88] 2.3.2 Interface Relaxation This method is based on the physical world relations among the parts of the model and follows the natural way the modeled event or process evolves. The local phenomenon in each subdomain obeys a local physical law modeled by a single PDE. The conditions ....
.... find new interface values) RVY93] ffl simplification of the least squares method by McFaddin [MR92b] ffl discrete Newton s method for the interface problem [Ric89] ffl Robin interface conditions (use a convex combination of Dirichlet and Neumann data as Robin interface conditions) Lio90, DH96] ffl Schur complement (alternate Dirichlet and Neumann data in space) FQZ88] 28 ffl shooting method for solving ODEs (solve a defect equation on the interface using Picard iteration to obtain the solution) Lai92] ffl Steklov Poincare operator method (alternate Dirichlet on the PDEs and ....
J. Douglas and C.-S. Huang. An Accelerated Domain Decomposition Procedure Based on Robin Transmission Conditions. Technical Report TR-289, Center for Applied Mathematics, Purdue University, 1996.
Accelerated Domain Decomposition Iterative Procedures for - Mixed Methods Based Self-citation (Douglas Huang) (Correct)
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J. Douglas, Jr., and C.-S. Huang. An accelerated domain decomposition procedure based on Robin transmission conditions. To appear in BIT.
Research Overview And Future Plans - Huang (1997) Self-citation (Huang) (Correct)
....Douglas, Paes Leme, Roberts, and Wang [8] did obtain convergence rates for fixed fi for a mixed finite element approximation of the elliptic boundary problem under a number of different hypotheses on the coefficients and the partition. Motivated by the ADI method, I co authored a paper [3] with Jim Douglas, Jr. that studies a version of Lions s iteration when the parameter fi depends on the iteration index. We treat the differential problem first and then consider a discrete approximation by the standard five point finite difference operator. For some model problems we introduce a ....
....based on the lowest index RaviartThomas space [11] over rectangles, when the parameter fi depends on the iteration index. We show that this version has similar convergence characteristics to those of the differential problem and to those of the finite difference problem in the case = 1 2 in [3]. Consequently, we show that a properly chosen parameter sequence can lead to a distinct speed up in the convergence rate for the iteration. Then, we show that a more significant acceleration of the iteration can be obtained by combining overlapping subdomains and the parameter cycle than by the ....
J. Douglas, Jr., and C.-S. Huang. An accelerated domain decomposition procedure based on Robin transmission conditions. BIT Numerical Mathematics, 37, pp. 678686, 1997.
Accelerated Domain Decomposition Iterative Procedures for.. - Douglas, Jr., Huang (1998) Self-citation (Douglas Huang) (Correct)
....to elliptic boundary problems was first introduced by P. L. Lions and later discussed by a number of authors under the assumption that the weighting of the flux and the trace of the solution in the Robin interface condition be independent of the iterative step number. Recently , the authors [6] studied a finite difference method for a Dirichlet problem and introduced a cycle of weights for the flux in this interface condition and proved that an acceleration in the convergence rate similar to that occurring for alternating direction iteration using a cycle of pseudo time steps results. ....
....the weighting fi of the normal derivatives in the transmission condition fi u j j u j = Gammafi u k k u k on the interface Gamma jk between subdomains Omega j and Omega k (as looked at from Omega j ) has been independent of the iterative index. Recently, the authors [6] have considered an extension in which the weighting has depended on the iterative index and have demonstrated for a model Dirichlet problem that a significant acceleration in the convergence rate of the iteration can be obtained by introducing a parameter cycle fi 1 ; fi n in place of ....
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J. Douglas, Jr., and C.-S. Huang. An accelerated domain decomposition procedure based on Robin transmission conditions. To appear in BIT.
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