A method is proposed for constructing local parametrizations of orthogonal bases and of subspaces by computing trajectories in the Stiefel and the Grassmann manifold, respectively. The trajectories are obtained by exp...
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ISBN:
(纸本)9783319399294;9783319399270
A method is proposed for constructing local parametrizations of orthogonal bases and of subspaces by computing trajectories in the Stiefel and the Grassmann manifold, respectively. The trajectories are obtained by exploiting sensitivity information on the singular value decomposition with respect to parametric changes and a Taylor-like local linearization suitably adapted to the underlying manifold structure. An important practical application of the proposed approach is parametric model reduction (pMOR). The connection with pMOR is discussed in detail and the results are illustrated by numerical experiment.
In this work, a framework for coupling arbitrary Lagrangian-Eulerian fluid-structure interaction with phase-field fracture is suggested. The key idea is based on applying the weak form of phase-field fracture, includi...
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ISBN:
(纸本)9783319399294;9783319399270
In this work, a framework for coupling arbitrary Lagrangian-Eulerian fluid-structure interaction with phase-field fracture is suggested. The key idea is based on applying the weak form of phase-field fracture, including a crack irreversibility constraint, to the nonlinear coupled system of Navier-Stokes and elasticity. The resulting setting is formulated via variational-monolithic coupling and has four unknowns: velocities, displacements, pressure, and a phase-field variable. The inequality constraint is imposed through penalization using an augmented Lagrangian algorithm. The nonlinear problem is solved with Newton's method. The framework is tested in terms of a numerical example in which computational stability is demonstrated by evaluating goal functionals on different spatial meshes.
This paper deals with flow induced vibrations of an elastic body. A simplified model of the human vocal fold is mathematically described. In order to consider the time dependent domain the arbitrary Lagrangian-Euleria...
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ISBN:
(纸本)9783319399294;9783319399270
This paper deals with flow induced vibrations of an elastic body. A simplified model of the human vocal fold is mathematically described. In order to consider the time dependent domain the arbitrary Lagrangian-Eulerian method is used. The viscous incompressible fluid flow and linear elasticity models are considered. The developed numerical schemes for the fluid flow and the elastic body are implemented by the in-house developed solver based on the finite element method. Preliminary numerical results testing the convergence of solver are presented.
In this study we deal with a problem of particulate matter dispersion modelling in a presence of a vegetation. We present a method to evaluate the efficiency of the barrier and to optimize its parameters. We use a CFD...
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ISBN:
(纸本)9783319399294;9783319399270
In this study we deal with a problem of particulate matter dispersion modelling in a presence of a vegetation. We present a method to evaluate the efficiency of the barrier and to optimize its parameters. We use a CFD solver based on the RANS equations to model the air flow in a simplified 2D domain containing a vegetation block adjacent to a road, which serves as a source of the pollutant. Modelled physics captures the processes of a gravitational settling of the particles, dry deposition of the particles on the vegetation, turbulence generation by the road traffic and effect of the vegetation on the air flow. To optimize the effectivity of the barrier we employ a gradient based optimization process. The results show that the optimized variant relies mainly on the effect of increased turbulent diffusion by a sparse vegetation and less on the dry deposition of the pollutant on the vegetation.
We present new sparse-grid based algorithms for fast Bayesian estimation and inversion of parametric operator equations. We propose Reduced Basis (RB) acceleration of numerical integration based on Smolyak sparse grid...
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ISBN:
(数字)9783319282626
ISBN:
(纸本)9783319282626;9783319282602
We present new sparse-grid based algorithms for fast Bayesian estimation and inversion of parametric operator equations. We propose Reduced Basis (RB) acceleration of numerical integration based on Smolyak sparse grid quadrature. To tackle the curse-of-dimensionality in high-dimensional Bayesian inversion, we exploit sparsity of the parametric forward solution map as well as of the Bayesian posterior density with respect to the random parameters. We employ an dimension adaptive Sparse Grid method (aSG) for both, offline-training the reduced basis as well as for deterministic quadrature of the conditional expectations which arise in Bayesian estimates. For the forward problem with nonaffine dependence on the random variables, we perform further affine approximation based on the Empirical Interpolation Method (EIM) proposed in [1]. A novel combined algorithm to adaptively refine the sparse grid used for quadrature approximation of the Bayesian estimates, of the reduced basis approximation and to compress the parametric forward solutions by empirical interpolation is proposed. The theoretically predicted computational efficiency which is independent of the number of active parameters is demonstrated in numerical experiments for a model, nonaffine-parametric, stationary, elliptic diffusion problem, in two spacial and in parameter space dimensions up to 1024.
Recently, we showed in (O. Kolb, SIAM J. Numer. Anal., 52 (2014), pp. 2335-2355) for which parameter range the compact third order WENO reconstruction procedure introduced in (D. Levy, G. Puppo, and G. Russo, SIAM J. ...
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ISBN:
(纸本)9783319399294;9783319399270
Recently, we showed in (O. Kolb, SIAM J. Numer. Anal., 52 (2014), pp. 2335-2355) for which parameter range the compact third order WENO reconstruction procedure introduced in (D. Levy, G. Puppo, and G. Russo, SIAM J. Sci. Comput., 22 (2000), pp. 656-672) reaches the optimal order of accuracy (h(3) in the smooth case and h(2) near discontinuities). This is the case for the parameter choice epsilon = Kh(q) in the weight design with q <= 3 and pq >= 2, where p >= 1 is the exponent used in the computation of the weights in theWENO scheme. While these theoretical results for the convergence rates of theWENO reconstruction procedure could also be validated in the numerical tests, the application within the semi-discrete central scheme of (A. Kurganov, and D. Levy, SIAM J. Sci. Comput., 22 (2000), pp. 1461-1488) together with a third order TVD-Runge-Kutta scheme for the time integration did not yield a third order accurate scheme in total for q > 2. The aim of this follow-up paper is to explain this observation with further analytical and numerical results.
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