Fluid-structure interaction problems involve material parameters such as the shear modulus of the solid and the dynamic fluid viscosity. In order to examine the behaviors of various solids and adapt the problems to di...
Fluid-structure interaction problems involve material parameters such as the shear modulus of the solid and the dynamic fluid viscosity. In order to examine the behaviors of various solids and adapt the problems to different fluid configurations there is a need to vary such material parameters flexibly. This can be done by a parameter-dependent fluid-structure interaction discretization which yields a system matrix that has block diagonal structure. As also discussed in [2], the resulting equation is equivalent to a matrix equation which allows for a low-rank approach where the iterate is represented by a tensor. A low-rank GMRES variant similar to what was discussed in [1] can then be applied to such parameter-dependent systems.
The cross Gramian matrix encodes the input-output coherence of linear controlsystems and is used in projection-based model reduction. The empirical cross Gramian is a data-driven variant of the cross Gramian which al...
We investigate the numerical solution to a low rank perturbed Lyapunov equation AT X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], b...
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Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of the...
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We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical ...
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Many problems in computational science and engineering are simultaneously characterized by the following challenging issues: uncertainty, nonlinearity, nonstationarity and high dimensionality. Existing numerical techn...
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Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time-varying systems and many more. Here, we will f...
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This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochas...
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In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider incl...
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In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle *** propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.
Model reduction methods for bilinear controlsystems are compared by means of practical examples of Liouville-von Neumann and Fokker-Planck type. methods based on balancing generalized system Gramians and on minimizin...
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