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Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

Milan Práger (1998)

Applications of Mathematics

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.

Error estimates for the Coupled Cluster method

Thorsten Rohwedder, Reinhold Schneider (2013)

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

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...

Estimate of vegetation efficiency on reducing dust concentration produced by a surface coal mine

Řezníček, Hynek, Beneš, Luděk (2019)

Programs and Algorithms of Numerical Mathematics

A new vegetative barrier can help to reduce dust concentration in a surface coal mine neighbourhood. The project reports about quantification of this effect. An air flow field is computed together with the dust transport driven by it using an in-house CFD solver. The 2D cuts of a real geometry of Bílina coal mine in north Bohemia are used. The vegetation is modelled as horizontally homogeneous porous medium which slows the air flow inside. An influence on turbulence and filtering the dust particles...

Event-triggered H ∞ static output feedback control of discrete time piecewise-affine systems

Zhuyun Xue, Mouquan Shen (2021)

Kybernetika

This paper is concerned with the problem of H ∞ event-triggered output feedback control of discrete time piecewise-affine systems. Relying on system outputs, a piecewise-affine triggering condition is constructed to release communication burden. Resorting to piecewise Lyapunov functional and robust control techniques, sufficient conditions are built to ensure the closed-loop systems to be asymptotically stable with the prescribed H ∞ performance. By utilizing a separation strategy, the static output...

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