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Block Gauss (block + gauss)
Selected AbstractsA parallel multigrid solver for high-frequency electromagnetic field analyses with small-scale PC clusterELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 9 2008Kuniaki Yosui Abstract Finite element analyses of electromagnetic fields are commonly used for designing various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is quite a useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high-frequency electromagnetic analyses, a special block Gauss, Seidel smoother is used for the multigrid solver instead of general smoothers such as a Gauss, Seidel or Jacobi smoother in order to improve the convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical example shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPUs was increased from one to five. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 91(9): 28, 36, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10160 [source] Analysis of the block Gauss,Seidel solution procedure for a strongly coupled model problem with reference to fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009M. M. Joosten Abstract The block Gauss,Seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid,structure interaction. Based on a simple model problem, this work presents a detailed analysis of the convergence behaviour of the method. In particular, the model problem is used to highlight some aspects that arise in the context of the application of the block Gauss,Seidel method to FSI problems. Thus, the effects of the time integration schemes chosen, of relaxation techniques, of physical constraints and non-linearities on the convergence of the iterations are investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source] An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materialsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2001Franz, Theo SuttmeierArticle first published online: 13 AUG 200 Abstract In this article, a mixed finite element formulation is described for coping with (nearly) incompressible behavior in elasto-plastic problems. In addition to the displacements, an auxiliary variable, playing the role of a pressure, is introduced resulting in Stokes-like problems. The discretization is done by a stabilized conforming Q1/Q1 -element, and the corresponding algebraic systems are solved by an adaptive multigrid scheme using a smoother of block Gauss,Seidel type. The adaptive algorithm is based on the general concept of using duality arguments to obtain weighted a posteriori error bounds. This procedure is carried out here for the described discretization of elasto-plastic problems. Efficiency and reliability of the proposed adaptive method is demonstrated at (plane strain) model problems. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:369,382, 2001 [source] | ||||||||||