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The Global ETD Search service is a free service for researchers
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Showing 1 to 10 of 10 (0.263 seconds)Spelling suggestions: "subject:"MSC 65010"" "subject:"MSC 652010""
| 1 |
Implicit extrapolation methods for multilevel finite element computationsJung, M., Rüde, U. 30 October 1998 (has links) (PDF)
Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.
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| 2 |
Some Remarks on the Constant in the Strengthened C.B.S. Inequality: Application to $h$- and $p$-Hierarchical Finite Element Discretizations of Elasticity ProblemsJung, M., Maitre, J. F. 30 October 1998 (has links) (PDF)
For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75.
For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements.
Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.
|
| 3 |
A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links) (PDF)
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.
|
| 4 |
A parallel preconditioned iterative realization of the panel method in 3DPester, M., Rjasanow, S. 30 October 1998 (has links) (PDF)
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.
|
| 5 |
Implicit extrapolation methods for multilevel finite element computationsJung, M., Rüde, U. 30 October 1998 (has links)
Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.
|
| 6 |
A parallel preconditioned iterative realization of the panel method in 3DPester, M., Rjasanow, S. 30 October 1998 (has links)
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.
|
| 7 |
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal controlPenzl, T. 30 October 1998 (has links) (PDF)
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
|
| 8 |
A parallel version of the preconditioned conjugate gradient method for boundary element equationsPester, M., Rjasanow, S. 30 October 1998 (has links)
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.
|
| 9 |
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal controlPenzl, T. 30 October 1998 (has links)
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
|
| 10 |
Some Remarks on the Constant in the Strengthened C.B.S. Inequality: Application to $h$- and $p$-Hierarchical Finite Element Discretizations of Elasticity ProblemsJung, M., Maitre, J. F. 30 October 1998 (has links)
For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75.
For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements.
Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.
|
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