Problems featuring moving interfaces appear in many applications. They can model solidification and melting of pure materials, crystal growth and other multi-phase problems. The control of the moving interface enables...
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate 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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The Bethe-Salpeter eigenvalue problem arises in the computation of the electronic structure of many-body physical systems. The resulting matrix is complex, admits a certain block structure and can become extremely lar...
The Bethe-Salpeter eigenvalue problem arises in the computation of the electronic structure of many-body physical systems. The resulting matrix is complex, admits a certain block structure and can become extremely large. This raises the need for structure-preserving algorithms running in parallel on high performance compute clusters. In this paper we examine how a recently proposed direct method given in the BSEPACK library can be improved using eigenvalue solvers from the ELPA library. For large matrices a runtime reduction of up to 80% is achieved.
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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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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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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