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Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations

Markus Stammberger, Heinrich Voss (2014)

Applications of Mathematics

Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.

Variational Gaussian process for optimal sensor placement

Gabor Tajnafoi, Rossella Arcucci, Laetitia Mottet, Carolanne Vouriot, Miguel Molina-Solana, Christopher Pain, Yi-Ke Guo (2021)

Applications of Mathematics

Sensor placement is an optimisation problem that has recently gained great relevance. In order to achieve accurate online updates of a predictive model, sensors are used to provide observations. When sensor location is optimally selected, the predictive model can greatly reduce its internal errors. A greedy-selection algorithm is used for locating these optimal spatial locations from a numerical embedded space. A novel architecture for solving this big data problem is proposed, relying on a variational...

Variational problems in domains with cusp points

Alexander Ženíšek (1993)

Applications of Mathematics

The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.

Variational sensitivity analysis of parametric Markovian market models

Norbert Hilber, Christoph Schwab, Christoph Winter (2008)

Banach Center Publications

Parameter sensitivities of prices for derivative contracts play an important role in model calibration as well as in quantification of model risk. In this paper a unified approach to the efficient numerical computation of all sensitivities for Markovian market models is presented. Variational approximations of the integro-differential equations corresponding to the infinitesimal generators of the market model differentiated with respect to the model parameters are employed. Superconvergent approximations...

Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study

Emilio Spedicato, Maria Teresa Vespucci (1993)

Applications of Mathematics

In this paper we compare the numerical performance on a set of ill conditioned problems of several algorithms for linear systems based upon the explicit QR factorization and the implicit LQ factorization associated with the Huang and the modified Huang algorithms in the ABS class. The results indicate that the modified Huang algorithm is generally more accurate than the Huang algorithm and competitive with commercial codes based upon the QR factorization with Householder of Givens reflections. The...

Verification of functional a posteriori error estimates for obstacle problem in 1D

Petr Harasim, Jan Valdman (2013)

Kybernetika

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.

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