406 research outputs found
An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems
We introduce in this paper a technique for the reduced order approximation of
parametric symmetric elliptic partial differential equations. For any given
dimension, we prove the existence of an optimal subspace of at most that
dimension which realizes the best approximation in mean of the error with
respect to the parameter in the quadratic norm associated to the elliptic
operator, between the exact solution and the Galerkin solution calculated on
the subspace. This is analogous to the best approximation property of the
Proper Orthogonal Decomposition (POD) subspaces, excepting that in our case the
norm is parameter-depending, and then the POD optimal sub-spaces cannot be
characterized by means of a spectral problem. We apply a deflation technique to
build a series of approximating solutions on finite-dimensional optimal
subspaces, directly in the on-line step. We prove that the partial sums
converge to the continuous solutions, in mean quadratic elliptic norm.Comment: 18 page
The Influence of Quadrature Errors on Isogeometric Mortar Methods
Mortar methods have recently been shown to be well suited for isogeometric
analysis. We review the recent mathematical analysis and then investigate the
variational crime introduced by quadrature formulas for the coupling integrals.
Motivated by finite element observations, we consider a quadrature rule purely
based on the slave mesh as well as a method using quadrature rules based on the
slave mesh and on the master mesh, resulting in a non-symmetric saddle point
problem. While in the first case reduced convergence rates can be observed, in
the second case the influence of the variational crime is less significant
Cork suberin as an additive in offset lithographic printing inks
Suberin oligomers, isolated from cork (Quercus suber L.), were used as additives in ‘Waterless’ and vegetable-oil ink formulations, in the range of 2–10% w/w. The rheological behaviour of the suberin oligomers as well as of the inks,
with and without suberin, were investigated as a function of temperature. It was shown that the addition of suberin
induces a decrease of viscosity of both inks. The tack of pristine inks, suberin oligomers and their mixtures were
determined at different temperatures: the variation of this parameter as a function of time provided information
about the drying kinetics of these formulations. The tack of the ‘Waterless’ ink was found to increase with the
introduction of suberin, whereas that of vegetable-oil based counterparts decreased. All the trends observed were
interpreted in terms of the differences in composition between the two types of inks. Preliminary printing tests were
carried out with the various suberin-containing inks.info:eu-repo/semantics/publishedVersio
Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics
We simulate the vibration of a violin bridge in a multi-query context using
reduced basis techniques. The mathematical model is based on an eigenvalue
problem for the orthotropic linear elasticity equation. In addition to the nine
material parameters, a geometrical thickness parameter is considered. This
parameter enters as a 10th material parameter into the system by a mapping onto
a parameter independent reference domain. The detailed simulation is carried
out by isogeometric mortar methods. Weakly coupled patch-wise tensorial
structured isogeometric elements are of special interest for complex geometries
with piecewise smooth but curvilinear boundaries. To obtain locality in the
detailed system, we use the saddle point approach and do not apply static
condensation techniques. However within the reduced basis context, it is
natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue
problem for a symmetric positive definite matrix. The selection of the
snapshots is controlled by a multi-query greedy strategy taking into account an
error indicator allowing for multiple eigenvalues
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