Relevant bibliographies by topics / MSC 65Y05, MSC 65N30

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Academic literature on the topic 'MSC 65Y05, MSC 65N30'

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Published: 4 June 2021
Last updated: 13 February 2022

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Dissertations / Theses on the topic "MSC 65Y05, MSC 65N30"

1

Apel, T., G. Haase, A. Meyer, and M. Pester. "Parallel solution of finite element equation systems: efficient inter-processor communication." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800670.

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This paper deals with the application of domain decomposition methods for the parallel solution of boundary value problems for partial differential equations over a domain $Omegabset R^d$, $d=2,3$. The attention is focused on the conception of efficient communication routines for the data exchange which is necessary for example in the preconditioned cg-algorithm for solving the resulting system of algebraic equations. The paper describes the data structure, different algorithms, and computational tests.
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2

Grabowsky, L., Th Ermer, and J. Werner. "Nutzung von MPI für parallele FEM-Systeme." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801365.

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Der Standard des Message Passing Interfaces (MPI) stellt dem Entwickler paralleler Anwendungen ein mächtiges Werkzeug zur Verfügung, seine Softwa- re effizient und weitgehend unabhängig von Details des parallelen Systems zu entwerfen. Im Rahmen einer Projektarbeit erfolgte die Umstellung der Kommunikationsbibliothek eines bestehenden FEM-Programmes auf den MPI-Mechanismus. Die Ergebnisse werden in der hier gegebenen Beschreibung der Cubecom-Implementierung zusammengefasst. In einem zweiten Teil dieser Arbeit wird untersucht, auf welchem Wege mit der in MPI verfügbaren Funktionalität auch die Koppelrandkommunikation mit einem einheitlichen und effizienten Verfahren durchgeführt werden kann. Sowohl fuer die Basisimplementierung als auch die MPI-basierte Koppelrandkommunikation wird die Effizienz untersucht und ein Ausblick auf weitere Anwendungsmoeglichkeiten gegeben.
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3

Groh, U. "Ein technologisches Konzept zur Erzeugung adaptiver hierarchischer Netze für FEM-Schemata." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800686.

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Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.
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4

Jung, M. "Parallelization of multi-grid methods based on domain decomposition ideas." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800781.

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In the paper, the parallelization of multi-grid methods for solving second-order elliptic boundary value problems in two-dimensional domains is discussed. The parallelization strategy is based on a non-overlapping domain decomposition data structure such that the algorithm is well-suited for an implementation on a parallel machine with MIMD architecture. For getting an algorithm with a good paral- lel performance it is necessary to have as few communication as possible between the processors. In our implementation, communication is only needed within the smoothing procedures and the coarse-grid solver. The interpolation and restriction procedures can be performed without any communication. New variants of smoothers of Gauss-Seidel type having the same communication cost as Jacobi smoothers are presented. For solving the coarse-grid systems iterative methods are proposed that are applied to the corresponding Schur complement system. Three numerical examples, namely a Poisson equation, a magnetic field problem, and a plane linear elasticity problem, demonstrate the efficiency of the parallel multi- grid algorithm.
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5

Meisel, Mathias, and Arnd Meyer. "Implementierung eines parallelen vorkonditionierten Schur-Komplement CG-Verfahrens in das Programmpaket FEAP." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800651.

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A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.
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6

Pester, M., and S. Rjasanow. "A parallel preconditioned iterative realization of the panel method in 3D." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800562.

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The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited also in three-dimensional case for implementation on a MIMD computer and that they are much more efficient than usual direct solution techniques.
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7

Pester, M. "Behandlung gekrümmter Oberflächen in einem 3D-FEM-Programm für Parallelrechner." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801386.

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The paper presents a method for generating curved surfaces of 3D finite element meshes by mesh refinement starting with a very coarse grid. This is useful for parallel implementations where the finest meshes should be computed and not read from large files. The paper deals with simple geometries as sphere, cylinder, cone. But the method may be extended to more complicated geometries. (with 45 figures)
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8

Pester, M., and S. Rjasanow. "A parallel version of the preconditioned conjugate gradient method for boundary element equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800455.

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The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.
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9

Reichel, U. "Partitionierung von Finite-Elemente-Netzen." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801107.

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The realization of the finite element method on parallel computers is usually based on a domain decomposition approach. This paper is concerned with the problem of finding an optimal decomposition and an appropriate mapping of the subdomains to the processors. The quality of this partitioning is measured in several metrics but it is also expressed in the computing time for solving specific systems of finite element equations. The software environment is first described. In particular, the data structure and the accumulation algorithm are introduced. Then several partitioning algorithms are compared. Spectral bisection was used with different modifications including Kernighan-Lin refinement, post-processing techniques and terminal propagation. The final recommendations should give good decompositions for all finite element codes which are based on principles similar to ours. The paper is a shortened English version of Preprint SFB393/96-18 (Uwe Reichel: Partitionierung von Finite-Elemente-Netzen), SFB 393, TU Chemnitz-Zwickau, December 1996. To be selfcontained, some material of Preprint SPC95_5 (see below) is included. The paper appeared as Preprint SFB393/96-18a, SFB 393, TU Chemnitz-Zwickau, January 1997.
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10

Ivanov, S. A., and V. G. Korneev. "On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800856.

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Abstract P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary re- sults for 1D case, condition number estimates and some inequalities for 2D reference element.
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