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Fast multigrid solver

Petr Vaněk (1995)

Applications of Mathematics

In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.

FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...

FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity

Axel Klawonn, Patrizio Neff, Oliver Rheinbach, Stefanie Vanis (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP := sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is...

Filter factors of truncated TLS regularization with multiple observations

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2017)

Applications of Mathematics

The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems A x b were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of A applied to b . This paper focuses on the situation...

Finding a Hamiltonian cycle using the Chebyshev polynomials

Lamač, Jan, Vlasák, Miloslav (2025)

Programs and Algorithms of Numerical Mathematics

We present an algorithm of finding the Hamiltonian cycle in a general undirected graph by minimization of an appropriately chosen functional. This functional depends on the characteristic polynomial of the graph Laplacian matrix and attains its minimum at the characteristic polynomial of the Laplacian matrix of the Hamiltonian cycle.

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