G. Molnárka

6506224081

Publications - 18

Modelling and Sensitivity Analysis of Nonlinear Firefighting Systems Using Maple

F. Hajdu Rajmund Kuti G. Molnárka

Publication Name: Communications in Computer and Information Science

Publication Date: 2021-01-01

Volume: 1414

Issue: Unknown

Page Range: 234-251

Description:

Mathematical modelling and numerical simulations have greatly contributed to the development of technical sciences in the recent decades. With powerful tools, like Maple, the examination of ever newer engineering applications in simulation environment was made possible. This paper gives an overview of mathematical modelling and numerical examination of nonlinear fire truck suspension systems using Maple. The examined models are the suspension system of a heavy-duty fire truck with different degrees of freedom and a special double-cabin fire truck suspension system with a crew compartment. The construction of mathematical models, their implementation to Maple and the numerical simulation results are explained. Detailed One-at-a-Time sensitivity analysis results using a novel fuzzy logic based evaluation method developed in Maple are also presented. With the proposed method an extended parameter range can be examined and the parameters can be easily compared. From the sensitivity analysis it was concluded that the spring characteristics and the road models greatly affect simulation results.

Open Access: Yes

DOI: 10.1007/978-3-030-81698-8_16

Testing output variables for sensitivity study of nonlinear vibration systems

F. Hajdu G. Molnárka

Publication Name: Pollack Periodica

Publication Date: 2020-08-01

Volume: 15

Issue: 2

Page Range: 70-81

Description:

In this study the detailed One-at-a-Time sensitivity analysis of nonlinear massspring- damper systems is carried out with numerical simulation. The degree of sensitivity was measured with a sensitivity index and based on its sensitivity Fuzzy-sets were established. The sensitivity of a parameter then can be expressed by the membership to the Fuzzy-sets. In this study the root mean square of acceleration, the maximum amplitude of acceleration and the peak frequency were chosen as output variables to measure sensitivity. With this research it was proven, that the root mean square of acceleration and the peak frequency can be used for sensitivity study of nonlinear vibration systems effectively.

Open Access: Yes

DOI: 10.1556/606.2020.15.2.7

One-at-a-time sensitivity study of a nonlinear fire truck suspension model

F. Hajdu Rajmund Kuti G. Molnárka

Publication Name: Fme Transactions

Publication Date: 2020-01-01

Volume: 48

Issue: 1

Page Range: 90-95

Description:

In this paper the detailed OAT (one-at-a-time) sensitivity analysis of a nonlinear fire truck suspension system is carried out with numerical simulation. As output to measure sensitivity the RMS of acceleration was chosen, which can be calculated with numerical simulations easily. The degree of sensitivity was measured with a sensitivity index and based on it sensitivity Fuzzy-sets were established. The membership of each parameter to the Fuzzy sets is calculated and based on it, it was determined which parameters are the most sensitive. With the presented results it is shown that the proposed method is suitable for testing mathematical models as well.

Open Access: Yes

DOI: 10.5937/fmet2001090H

Parallelization of numerical examination of nonlinear systems using maple

F. Hajdu G. Molnárka

Publication Name: Civil Comp Proceedings

Publication Date: 2017-01-01

Volume: 111

Issue: Unknown

Page Range: Unknown

Description:

In this work we present possibilities of the parallelization of numerical examination and simulation of nonlinear systems, especially creating phase-plane diagrams in parallel. For construction of such diagrams Maple was used because it provides algorithms for solving differential equations and two models for parallelization. These are the Task programming model and the Grid programming model. The paper describes the development, the test and the comparison of the parallel programs created according to the two parallelization models. Even using a simple desktop with low number of processors a relative good speedup with a good efficiency could be achieved in both cases. It was also examined how the problem size affects the speedup and the efficiency.

Open Access: Yes

DOI: DOI not available

Optimal die design in extrusion process using adaptive finite element method

A. Lotfi G. Molnárka

Publication Name: Aip Conference Proceedings

Publication Date: 2009-11-26

Volume: 1168

Issue: Unknown

Page Range: 324-328

Description:

In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by an adaptive finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B-spline functions allow us to determine the shape of the die, using its control points as design variables. An adaptive solution procedure is adapted to control the error due to the finite element approximation. The mesh adaptation is performed using the Zienkiewicz - Zhu (Z2) type error estimator. © 2009 American Institute of Physics.

Open Access: Yes

DOI: 10.1063/1.3241460

A simultaneous solution for general linear equations with subspace decomposition

N. Varjasi G. Molnárka

Publication Name: Civil Comp Proceedings

Publication Date: 2011-01-01

Volume: 95

Issue: Unknown

Page Range: Unknown

Description:

For solving linear systems of equations there are several known algorithms. For large linear systems with a sparse matrix iteration algorithms are recommended. But in the case of general n x m matrices the classic iterative algorithms are not applicable with a few exceptions. For example in some cases the Lanczos type algorithms are adequate. The algorithm presented here based is on the minimization of residual solution with subspace decomposition. Therefore this algorithm seems to be applicable for the construction of parallel algorithms. In this paper we describe a sequential version of proposed algorithm first and give its theoretical analysis. The algorithm has some genetic characteristics. After this we will formulate a parallel version of algorithm with subspace decomposition in order to study the details of convergence and the speed up effect of the parallel algorithms. The numerical test results of these algorithms including the speed-up effects of the parallel execution will be shown. The comparison of the classical method and the new approach will also be presented considering the running speed and efficiency too. The computer tests have been carried out with parallel and cluster computing methods as well. © Civil-Comp Press, 2011.

Open Access: Yes

DOI: DOI not available

Half-magnitude extensions of resolution and field of view in digital holography by scanning and magnification

A. Lotfi Attila Tibor Nagy István Harmati Béla Ráczkevi György Molnar Dezsö Szigethy Attila Nagy G. Molnárka Venczel Borbély Ferenc Gyímesi Aladar Czitrovszky Zoltán Füzessy

Publication Name: Applied Optics

Publication Date: 2009-11-01

Volume: 48

Issue: 31

Page Range: 6026-6034

Description:

Digital holography replaces the permanent recording material of analog holography with an electronic light sensitive matrix detector, but besides the many unique advantages, this brings serious limitations with it as well. The limited resolution of matrix detectors restricts the field of view, and their limited size restricts the resolution in the reconstructed holographic image. Scanning the larger aerial hologram (the interference light field of the object and reference waves in the hologram plane) with the small matrix detector or using magnification for the coarse matrix detector at the readout of the fine-structured aerial hologram, these are straightforward solutions but have been exploited only partially until now. We have systematically applied both of these approaches and have driven them to their present extremes, over half a magnitude in extensions. © 2009 Optical Society of America.

Open Access: Yes

DOI: 10.1364/AO.48.006026

Solving contact problems using the domain decomposition method with an interface preconditioner

A. Lotfi G. Molnárka

Publication Name: Proceedings of the 6th International Conference on Engineering Computational Technology

Publication Date: 2008-12-01

Volume: Unknown

Issue: Unknown

Page Range: Unknown

Description:

The present paper is concerned with the frictionless bilateral or unilateral contact problem between two elastic bodies. An algorithm is introduced to solve the resulting finite element system by a non-overlapping domain decomposition method. This technique enable us to transform the solution of the global problem to the solutions of the elasticity equations for each body separately and the solution of the Schur complement problem on the contact surface. The main goal of this work is the construction of the interface preconditioner for the Schur complement problem. The solution is obtained by using a successive approximation method. Finally, some numerical results of the proposed method are given. © 2008 Civil-Comp Press.

Open Access: Yes

DOI: DOI not available

A mathematical model for the middle ear ventilation

G. Molnárka M. Fücsek E. Miletics

Publication Name: Aip Conference Proceedings

Publication Date: 2008-10-22

Volume: 1046

Issue: Unknown

Page Range: 106-109

Description:

The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([1]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation. © 2008 American Institute of Physics.

Open Access: Yes

DOI: 10.1063/1.2997288

A scalable parallel genetic algorithm for solving linear systems

G. Molnárka

Publication Name: Proceedings of the 5th International Conference on Engineering Computational Technology

Publication Date: 2006-12-01

Volume: Unknown

Issue: Unknown

Page Range: Unknown

Description:

For solving linear system of equations is known several algorithms. Iteration algorithms are recommended for the large linear systems with sparse matrix. But in the case of general non-symmetrical or n x m matrices the classic iterative algorithms are not applicable with a few exceptions. For example in some cases the Lanczos type algorithms are adequate. The algorithm presented here based on the minimization of square of residuum of approximate solution and it has some genetic character. Therefore this algorithm seems to be applicable for construction of parallel algorithm. Here we describe a parallel version of proposed algorithm and give its theoretical analysis. © 2006 Civil-Comp Press.

Open Access: Yes

DOI: DOI not available

Implicit extension of Taylor series method with numerical derivatives for initial value problems

G. Molnárka E. Miletics

Publication Name: Computers and Mathematics with Applications

Publication Date: 2005-10-01

Volume: 50

Issue: 7

Page Range: 1167-1177

Description:

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval integration. This property offers different facility for adaptive error control. This paper describes several explicit Taylor series algorithms with numerical derivatives and their implicit extension and examines its consistency and stability properties. The implicit extension based on a collocation term added to the explicit truncated Taylor series and the approximate solution obtained as a continuously differentiable piecewise polynomials function. Some numerical test results is presented to prove the efficiency of these new-old algorithm. © 2005 Elsevier Ltd. All rights reserved.

Open Access: Yes

DOI: 10.1016/j.camwa.2005.08.017

Implicit extension of taylor series method for initial value problems

G. Molnárka

Publication Name: Journal of Computational Methods in Sciences and Engineering

Publication Date: 2005-01-01

Volume: 5

Issue: 4

Page Range: 263-270

Description:

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval. This property offers different facility for adaptive error control. This paper describes several explicit Taylor series with implicit extension algorithms and examines its consistency and stability properties. The implicit extension based on a collocation term added to the explicit truncated Taylor series. This idea is different from the general collocation method construction, which conduces to the implicit R-K algorithms [12]. It demonstrates some numerical test results for stiff systems herewith we attempt to prove the efficiency of these new-old algorithms.

Open Access: Yes

DOI: 10.3233/jcm-2005-5404

Taylor series method with numerical derivatives for initial value problems

G. Molnárka E. Miletics

Publication Name: Journal of Computational Methods in Sciences and Engineering

Publication Date: 2004-01-01

Volume: 4

Issue: 1-2

Page Range: 105-114

Description:

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations. In some cases such algorithms will be much more complicated than a R-K methods, because it will require more function evaluation than well-known classical algorithms. However these evaluations can be accomplished fully parallel and the coefficients of truncated Taylor series can be calculated with matrix-vector operations. For large systems these operations suit for the parallel computers. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval and the local error of this solution at the interior points of the subinterval is less than that one at the end point. This property offers different facility for adaptive error control. This paper describes several above-mentioned algorithms and examines its consistency and stability properties. It demonstrates some numerical test results for stiff systems herewith we attempt to prove the efficiency of these new-old algorithms.

Open Access: Yes

DOI: 10.3233/jcm-2004-41-213

The method of asymptotic expansion for plate problem in the linear theory of viscoelasticity

A. Lotfi G. Molnárka

Publication Name: ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik

Publication Date: 2000-01-01

Volume: 80

Issue: 4 SUPPL. 2

Page Range: S391-S392

Description:

The method of asymptotic expansion originally developed for elasticity problems is generalized to linear viscoelastic problems. Three-dimensional, unsteady problems corresponding to a class of viscoelastic plates are considered. By employing the Laplace transform, the original problem is converted to an equivalent elastic problem, where the asymptotic expansion method is used. An application of this method to the Maxwell model is also presented.

Open Access: Yes

DOI: 10.1002/zamm.20000801467

Calculation of the optimal shape of nonconical dies by minimizing necessary forces

E. Halbritter G. Molnárka

Publication Name: Advances in Engineering Software

Publication Date: 1999-09-15

Volume: 30

Issue: 9-11

Page Range: 735-740

Description:

A mathematical model is given for the metal forming in an axisymmetric nonconical converging die. By using the Maple V system a semianalytical algorithm is proposed for the calculation of the optimal shape of the die which minimizes the consumed energy of the deformation and the power of the friction forces at the wall. Two examples are presented to demonstrate the efficiency of the proposed method. © 1999 Elsevier Science Ltd and Civil-Comp Ltd. All rights reserved.

Open Access: Yes

DOI: 10.1016/S0965-9978(98)00117-3

Residual elimination algorithm for solving linear equations and application for sparse systems

B. Török G. Molnárka

Publication Name: ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik

Publication Date: 1996-12-01

Volume: 76

Issue: SUPPL. 1

Page Range: 485-486

Description:

A new direct algorithm for solving linear system of equations will be presented. Short theoretical background and analysis of the proposed method will be given. We formulate an optimized version of the proposed algorithm, which also works for sparse matrices. The complexity of the suggested algorithm for full matrix systems is n3/3 H- O(n2) where n is the dimension of the problem. The numerical experiments show that some versions of the residual elimination algorithm can be competitive with the Gaussian elimination both in complexity and precision. Moreover the sparse linear solver based on this algorithm has some advantages in parallel environment.

Open Access: Yes

DOI: DOI not available

A block-circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems by second order finite elements

B. Kiss G. Molnárka

Publication Name: Computing Systems in Engineering

Publication Date: 1995-01-01

Volume: 6

Issue: 4-5

Page Range: 369-376

Description:

A preconditioned conjugate gradient domain decomposition method was given Refs 1 and 2 for the solution of a system of linear equations arising in the finite element method applied to the elliptic Dirichlet, Neumann and mixed boundary value problems. We have proved that the construction can be generalized2 for higher order finite element method. Here we give a construction and theoretical investigation of preconditioners for second order finite elements. A method and the the results of calculation is given. The presented numerical experiments show that this preconditioner works well. © 1995.

Open Access: Yes

DOI: 10.1016/0956-0521(95)00039-9

A circulant preconditioner for domain decomposition algorithm for the solution of the elliptic problems

N. A.A. Rahman B. Kiss G. Molnárka

Publication Name: Periodica Mathematica Hungarica

Publication Date: 1994-08-01

Volume: 29

Issue: 1

Page Range: 67-80

Description:

A preconditioned conjugate gradient (PCG)-based domain decomposition method was given in [11] and [12] for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed algorithm was that the recommended preconditioner was constructed by using symmetric-cyclic matrix. But we could give only the definitions of the entries of this cyclic matrix. Here we give a short description of this algorithm, the method of calculation of matrix entries and the results of calculation. The numerical experiments presented show, that this construction of precondition in the practice works well. © 1994 Akadémiai Kiadó.

Open Access: Yes

DOI: 10.1007/BF01876204