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1
Content available Finite-Difference Operators for 2D problems
Sobczyk T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2020
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Vol. 68, nr 6
1535--1541
EN
This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.
2
Content available Improved algorithm for periodic steady-state analysis in nonlinear electromagnetic devices
Sobczyk T. J., Radzik M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
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Vol. 67, nr 5
863--869
EN
This paper presents the improved methodology for the direct calculation of steady-state periodic solutions for electromagnetic devices, as described by nonlinear differential equations, in the time domain. A novel differential operator is developed for periodic functions and the iterative algorithm determining periodic steady-state solutions in a selected set of time instants is identified. Its application to steady-state analysis is verified by an elementary example. The modified algorithm reduces the complexity of steady-state analysis, particularly for electromagnetic devices described by high-dimensional nonlinear differential equations.
3
Content available Application of novel discrete differential operator of periodic function to study electromechanical interactions
Sobczyk T. J., Radzik M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
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Vol. 66, nr 5
645--653
EN
This paper investigates an algorithm for finding steady-states in electromechanical systems for the cases of their periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain. The basis for such an algorithm is a discrete differential operator that specifies the values of the first derivative of the periodic function in the selected set of points on the basis of the values of that function in the same set of points. It creates algebraic equations describing the steady-state solution for the nonlinear differential equations describing electromechanical systems. In this paper, the direct time-domain approach is tested for the simple converter considering. The algorithm used in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.
4
Content available Algorithm for determining two-periodic steady-states in AC machines directly in time domain
Sobczyk T.J.
Archives of Electrical Engineering
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2016
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Vol. 65, nr 3
575--583
EN
This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the twoperiodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.
5
Content available remote Iterative algorithm for determining distribution of porosity of material in cooling channels of gas turbine blades
Frąckowiak A.
Journal of Mechanical and Transport Engineering
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2015
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Vol. 67, No. 1
23--36
EN
This paper presents an iterative algorithm for determining the porosity distribution of a material filling cooling channels in the gas turbine blades. The objective of numerical simulations employing this algorithm was to obtain the assumed temperature distribution on the inner boundary of the blade (walls of the cooling channels). Calculations were performed for the region of an elliptic ring, for which the analytical solution was known. Numerical calculations in the region of the elliptical ring showed a very high consistency of numerical results with the analytical solution. Results of calculations indicate that employing this algorithm for the optimization of the gas turbine blades cooling process is highly practical.
PL
W artykule przedstawiono algorytm iteracyjny do wyznaczania rozkładu porowatości materiału wypełniającego kanały chłodzące łopatek turbin gazowych. Celem obliczeń numerycznych, wykonanych za pomocą tego algorytmu, było uzyskanie zakładanego rozkładu temperatury na wewnętrznym brzegu łopatki (ścianach kanałów chłodzących). Obliczenia wykonano dla obszaru pierścienia eliptycznego, w którym znane było rozwiązanie analityczne. Obliczenia numeryczne w obszarze pierścienia eliptycznego wykazały bardzo dobrą zgodność wyników numerycznych z rozwiązaniem analitycznym. Wyniki obliczeń wskazują na duże praktyczne zastosowanie tego algorytmu do optymalizacji chłodzenia łopatek turbin gazowych.
6
Content available remote Iterative estimators of parameters in linear models with partially variant coefficients
Hu S., Meinke K., Chen R., Huajiang O.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 2
179-187
EN
A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and applicable in practical fields.
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