Spelling suggestions: "subject:"finiteelementmethod."" "subject:"randelementemethode.""
251 |
Parabolische Randanfangswertprobleme mit zufälliger AnfangsbedingungKandler, Anne, Richter, Matthias, vom Scheidt, Jürgen 07 October 2005 (has links) (PDF)
In dieser Arbeit werden parabolische Randanfangswertprobleme mit zufälliger
Anfangs- und Neumann-Randbedingung betrachtet. Die zufälligen Einflußgrößen
werden dabei als epsilon-korrelierte, zufällige Felder modelliert. Das Hauptinteresse liegt
auf der Berechnung stochastischer Kenngrößen der auf Basis der Finite-Elemente
Methode erhaltenen Lösung des Randanfangswertproblems. Für die Korrelationsfunktion
der Lösung wird eine Entwicklung nach der Korrelationslänge sowie eine
explizite Berechnung für spezielle Typen der Vernetzung vorgestellt. Anhand von
numerischen Beispielen werden abschließend die auf den verschiedenen Wegen erhaltenen
Varianzen mit der einer simulierten Lösung verglichen.
|
252 |
Visualization Tools for 2D and 3D Finite Element Programs - User's ManualPester, Matthias 04 April 2006 (has links) (PDF)
This paper deals with the visualization of
numerical results as a very convenient method to
understand and evaluate a solution which has been
calculated as a set of millions of numerical values.
One of the central research fields of the Chemnitz
SFB 393 is the analysis of parallel numerical
algorithms for large systems of linear equations
arising from differential equations (e.g. in solid
and fluid mechanics). Solving large problems on
massively parallel computers makes it more and
more impossible to store numerical data from the
distributed memory of the parallel computer to
the disk for later postprocessing. However, the
developer of algorithms is interested in an
on-line response of his algorithms. Both visual
and numerical response of the running program may
be evaluated by the user for a decision how to
switch or adjust interactively certain parameters
that may influence the solution process.
The paper gives a survey of current programmer
and user interfaces that are used in our various
2D and 3D parallel finite element programs for
the visualization of the solution.
|
253 |
Fast solvers for degenerated problemsBeuchler, Sven 11 April 2006 (has links) (PDF)
In this paper, finite element discretizations of the
degenerated operator
-ω<sup>2</sup>(y) u<sub>xx</sub>-ω<sup>2</sup>(x)u<sub>yy</sub>=g
in the unit square are investigated, where the
weight function satisfies ω(ξ)=ξ<sup>α</sup>
with α ≥ 0.
We propose two multi-level methods in order to
solve the resulting system of linear algebraic
equations. The first method is a multi-grid
algorithm with line-smoother.
A proof of the smoothing property is given.
The second method is a BPX-like preconditioner
which we call MTS-BPX preconditioner.
We show that the upper eigenvalue bound of the
MTS-BPX preconditioned system matrix grows
proportionally to the level number.
|
254 |
Randkonzentrierte und adaptive hp-FEMEibner, Tino 12 July 2006 (has links) (PDF)
Die vorliegende Arbeit befasst sich mit verschiedenen Aspekten der hp-FEM.
Insbesondere werden hierbei folgende Punkte genauer untersucht:
1. Das effiziente Aufstellen der Steifigkeitsmatrix auf Referenzelementen, die keine Tensorproduktstruktur besitzen.
2. Eine lokale Konvergenzbetrachtung für die randkonzentrierte hp-FEM.
3. Ein Multilevel-Löser für die randkonzentrierte hp-FEM.
4. Eine Strategie für hp-Adaptivität.
|
255 |
Clément-type interpolation on spherical domains - interpolation error estimates and application to a posteriori error estimationApel, Thomas, Pester, Cornelia 31 August 2006 (has links) (PDF)
In this paper, a mixed boundary value problem for
the Laplace-Beltrami operator is considered for
spherical domains in $R^3$, i.e. for domains on
the unit sphere. These domains are parametrized
by spherical coordinates (\varphi, \theta),
such that functions on the unit sphere are
considered as functions in these coordinates.
Careful investigation leads to the introduction
of a proper finite element space corresponding to
an isotropic triangulation of the underlying
domain on the unit sphere. Error estimates are
proven for a Clément-type interpolation operator,
where appropriate, weighted norms are used.
The estimates are applied to the deduction of
a reliable and efficient residual error estimator
for the Laplace-Beltrami operator.
|
256 |
The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshesGrosman, Serguei 01 September 2006 (has links) (PDF)
Singularly perturbed reaction-diffusion problems
exhibit in general solutions with anisotropic
features, e.g. strong boundary and/or interior
layers. This anisotropy is reflected in the
discretization by using meshes with anisotropic
elements. The quality of the numerical solution
rests on the robustness of the a posteriori error
estimator with respect to both the perturbation
parameters of the problem and the anisotropy of the
mesh. The simplest local error estimator from the
implementation point of view is the so-called
hierarchical error estimator. The reliability
proof is usually based on two prerequisites:
the saturation assumption and the strengthened
Cauchy-Schwarz inequality. The proofs of these
facts are extended in the present work for the
case of the singularly perturbed reaction-diffusion
equation and of the meshes with anisotropic elements.
It is shown that the constants in the corresponding
estimates do neither depend on the aspect ratio
of the elements, nor on the perturbation parameters.
Utilizing the above arguments the concluding
reliability proof is provided as well as the
efficiency proof of the estimator, both
independent of the aspect ratio and perturbation
parameters.
|
257 |
Entwicklung von adaptiven Algorithmen für nichtlineare FEMBucher, Anke, Meyer, Arnd, Görke, Uwe-Jens, Kreißig, Reiner 01 September 2006 (has links) (PDF)
The development of adaptive finite element
procedures for the solution of geometrically
and physically nonlinear problems in structural
mechanics is very important for the augmentation
of the efficiency of FE-codes. In this contribution
methods of mesh refinement as well as mesh
coarsening are presented for a material model
considering finite elasto-plastic deformations.
For newly generated elements stresses, strains and
internal variables have to be calculated. This
implies the determination of the nodal values as
well as the Gaussian point values of the new
elements based on the transfer of data from the
former mesh. Analogously, the coarsening of less
important elements necessitates the determination
of these values for the newly created father
elements.
|
258 |
An adaptive strategy for hp-FEM based on testing for analyticityEibner, Tino, Melenk, Jens Markus 01 September 2006 (has links) (PDF)
We present an $hp$-adaptive strategy that is based
on estimating the decay of the expansion coefficients
when a function is expanded in $L^2$-orthogonal
polynomails on a triangle or a tetrahedron.
This method is justified by showing that the decay
of the coefficients is exponential if and only if
the function is analytic.
Numerical examples illustrate the performance of
this approach, and we compare it with two other
$hp$-adaptive strategies.
|
259 |
The Fourier-finite-element method with Nitsche-mortaringHeinrich, Bernd, Jung, Beate 01 September 2006 (has links) (PDF)
The paper deals with a combination of the
Fourier-finite-element method with the
Nitsche-finite-element method (as a mortar method).
The approach is applied to the Dirichlet problem
of the Poisson equation in three-dimensional
axisymmetric domains $\widehat\Omega$ with
non-axisymmetric data. The approximating Fourier
method yields a splitting of the 3D-problem into
2D-problems. For solving the 2D-problems on the
meridian plane $\Omega_a$,
the Nitsche-finite-element method with
non-matching meshes is applied. Some important
properties of the approximation scheme are
derived and the rate of convergence in some
$H^1$-like norm is proved to be of the type
${\mathcal O}(h+N^{-1})$ ($h$: mesh size on
$\Omega_a$, $N$: length of the Fourier sum) in
case of a regular solution of the boundary value
problem. Finally, some numerical results are
presented.
|
260 |
Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparisonEibner, Tino, Melenk, Jens Markus 11 September 2006 (has links) (PDF)
We analyze and compare different techniques to
set up the stiffness matrix in the hp-version
of the finite element method. The emphasis is
on methods for second order elliptic problems
posed on meshes including triangular and
tetrahedral elements. The polynomial degree
may be variable. We present a generalization
of the Spectral Galerkin Algorithm of [7],
where the shape functions are adapted to the
quadrature formula, to the case of
triangles/tetrahedra. Additionally, we study
on-the-fly matrix-vector multiplications, where
merely the matrix-vector multiplication is
realized without setting up the stiffness matrix.
Numerical studies are included.
|
Page generated in 0.0602 seconds