PUMA publications for /user/mhartmann/systems,https://puma.ub.uni-stuttgart.de/user/mhartmann/systems,PUMA RSS feed for /user/mhartmann/systems,2024-03-29T14:50:38+01:00Efficient a-posteriori error estimation for nonlinear kernel-based
reduced systemshttps://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmannmhartmann2018-07-20T10:54:15+02:00a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="D. Wirtz" itemprop="url" href="/person/1e80ae72fe2c1f9f79f4f7f8f5ce00735/author/0"><span itemprop="name">D. Wirtz</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="B. Haasdonk" itemprop="url" href="/person/1e80ae72fe2c1f9f79f4f7f8f5ce00735/author/1"><span itemprop="name">B. Haasdonk</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Systems and Control Letters</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">61 </span></span>(<span itemprop="issueNumber">1</span>):
<span itemprop="pagination">203 - 211</span></em> </span>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based
reduced systems612012a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig In this paper, we consider the topic of model reduction for nonlinear
dynamical systems based on kernel expansions. Our approach allows
for a full offline/online decomposition and efficient online computation
of the reduced model. In particular, we derive an a-posteriori state-space
error estimator for the reduction error. A key ingredient is a local
Lipschitz constant estimation that enables rigorous a-posteriori
error estimation. The computation of the error estimator is realized
by solving an auxiliary differential equation during online simulations.
Estimation iterations can be performed that allow a balancing between
estimation sharpness and computation time. Numerical experiments
demonstrate the estimation improvement over different estimator versions
and the rigor and effectiveness of the error bounds.A-posteriori error estimation for parameterized kernel-based systemshttps://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmannmhartmann2018-07-20T10:54:15+02:00a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Daniel Wirtz" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/0"><span itemprop="name">D. Wirtz</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Bernard Haasdonk" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/1"><span itemprop="name">B. Haasdonk</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
Modelling</span>, </em></span>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
ModellingA-posteriori error estimation for parameterized kernel-based systems2012a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig This work is concerned with derivation of fully offine/online decomposable
effcient aposteriori error estimators for reduced parameterized nonlinear
kernel-based systems. The dynamical systems under consideration consist
of a nonlinear, time- and parameter-dependent kernel expansion representing
the system's inner dynamics as well as time- and parameter-affne
inputs, initial conditions and outputs. The estimators are established
for a reduction technique originally proposed in [7] and are an extension
of the estimators derived in [11] to the fully time-dependent, parameterized
setting. Key features for the effcient error estimation are to use
local Lipschitz constants provided by a certain class of kernels
and an iterative scheme to balance computation cost against estimation
sharpness. Together with the affnely time/parameter-dependent system
components a full offine/online decomposition for both the reduction
process and the error estimators is possible. Some experimental results
for synthetic systems illustrate the effcient evaluation of the derived
error estimators for different parameters.Solvability and regularity results to boundary-transmission problems
for metallic and piezoelectric elastic materialshttps://puma.ub.uni-stuttgart.de/bibtex/2f0232cdd8fe2c486d6b1dc4dd272c951/mhartmannmhartmann2018-07-20T10:54:15+02:00Elliptic boundary-transmission elasticity piezoelectricity, potential problems systems, theory, vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="T. Buchukuri" itemprop="url" href="/person/1962a9ca8032fc89fea0d9f7026539fd0/author/0"><span itemprop="name">T. Buchukuri</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="O. Chkadua" itemprop="url" href="/person/1962a9ca8032fc89fea0d9f7026539fd0/author/1"><span itemprop="name">O. Chkadua</span></a></span>, </span><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="D. Natroshvili" itemprop="url" href="/person/1962a9ca8032fc89fea0d9f7026539fd0/author/2"><span itemprop="name">D. Natroshvili</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="A.-M. Sändig" itemprop="url" href="/person/1962a9ca8032fc89fea0d9f7026539fd0/author/3"><span itemprop="name">A. Sändig</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Mathematische Nachrichten</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">282 </span></span>(<span itemprop="issueNumber">8</span>):
<span itemprop="pagination">1079--1110</span></em> </span>(<em><span>2009<meta content="2009" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018Mathematische Nachrichten81079--1110Solvability and regularity results to boundary-transmission problems
for metallic and piezoelectric elastic materials2822009Elliptic boundary-transmission elasticity piezoelectricity, potential problems systems, theory, vorlaeufig We investigate three-dimensional transmission problems related to
the interaction of metallic and piezoelectric ceramic bodies. We
give a mathematical formulation of the physical problem when the
metallic and ceramic sub-domains are bonded along some proper parts
of their boundaries. The corresponding nonclassical mixed boundary-transmission
problem is reduced by the potential method to an equivalent nonselfadjoint
strongly elliptic system of pseudo-differential equations on manifolds
with boundary. We investigate the solvability of this system in different
function spaces. On the basis of these results we prove uniqueness
and existence theorems for the original boundary-transmission problem.
We study also the regularity of the electrical and mechanical fields
near the curves where the boundary conditions change and where the
interfaces intersect the exterior boundary. The electrical and mechanical
fields can be decomposed into singular and more regular terms near
these curves. A power of the distance from a reference point to the
corresponding edge-curves occurs in the singular terms and describes
the regularity explicitly. We compute these complex-valued exponents
and demonstrate their dependence on the material parameters (� 2009
WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim)