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Found 5152 publications

Multi-level biharmonic and bi-Helmholtz interpolation with application to the boundary element method

Csaba Gáspár

Publication Name: Engineering Analysis with Boundary Elements

Publication Date: 2000-01-01

Volume: 24

Issue: 7-8

Page Range: 559-573

Description:

The scattered data interpolation problem is investigated. Instead of the direct use of radial basis functions, the interpolation function is sought as a solution of a higher order partial differential equation supplied with the interpolation equations as special boundary conditions. In this paper the methods based on the biharmonic and the bi-Helmholtz equations are analyzed. The interpolation problem is reformulated in variational forms. Existence and uniqueness theorems are proved in Sobolev spaces. The approximation properties of this interpolation are also investigated. A representation theorem is proved which shows the similarity to the method of radial basis functions based on the fundamental solution of the applied partial differential operator. To solve the appearing biharmonic/bi-Helmholtz equation, a multi-level method is presented which is based on a quadtree/octtree cell system generated by the interpolation points. It is shown that the overall computational cost of the presented method is much less than that of the traditional method of radial basis functions. The method makes it possible to avoid the solution of large, fully populated and often ill-conditioned systems of linear equations. Finally, some applications to solving partial differential equations are outlined. The biharmonic/bi-Helmholtz interpolation technique immediately defines a grid-free method, but can be combined with the boundary element method as well. A possible application in the dual reciprocity method is also presented.

Open Access: Yes

DOI: 10.1016/S0955-7997(00)00036-9

On the negative weighting factors in the Muskingum-Cunge scheme

Sàndor Szél Csaba Gáspár

Publication Name: Journal of Hydraulic Research

Publication Date: 2000-01-01

Volume: 38

Issue: 4

Page Range: 299-306

Description:

The Muskingum-Cunge scheme applied to the one-dimensional unsteady advection-diffusion equation is investigated. To eliminate the numerical diffusion, the coefficients of the scheme are defined in such a way that the scheme does not contain the weighting parameters explicitly, but the Courant and Péclet numbers only. If one of the weighting factors is prescribed, the other should be necessarily negative in a lot of cases, which does not affect the applicability of the scheme. It is shown that the accuracy can be increased further, the numerical oscillations can also be eliminated by prescribing a simple relationship between the Courant and Péclet numbers. Sufficient conditions for strong stability are also presented.

Open Access: Yes

DOI: 10.1080/00221680009498329

On commutative asynchronous nondeterministic automata

A. Pukler M. Ito B. Imreh

Publication Name: Acta Cybernetica

Publication Date: 2000-01-01

Volume: 14

Issue: 4

Page Range: 607-617

Description:

In this paper, we deal with nondeterministic automata, in particular, commutative asynchronous ones. Our goal is to give their isomorphic representation under the serial product or equivalently, under the α0-product. It turns out that this class does not contain any finite isomorphically complete system with respect to the α0-product. On the other hand, we present an isomorphically complete system for this class which consists of one monotone nondeterministic automaton of three elements.

Open Access: Yes

DOI: DOI not available

Influence of weediness on sugar beet yields

Péter Bosák Katalin Lajos

Publication Name: Novenytermeles

Publication Date: 1999-12-01

Volume: 48

Issue: 6

Page Range: 617-629

Description:

The influence of weeds on yield and quality were studied in sugar beet stands kept mechanically weedless for different periods in small-plot. Plots which were weeded early in the season (1st May or 15th May) and were kept clean to the end of the growing period (30th September) gave significantly higher and better quality yield than plots where weed killing started later (1st June) or where the weeds were allowed to reappear after 15th May or 1st June. Trials proved that weed control in sugar beet has to be started early and that the stand has to be kept weedless to the end of the growing period. The late spread of weeds is an important yield-reducing factor.

Open Access: Yes

DOI: DOI not available

The influence of hydrogen molecules on shock-cloud collisions

U. Ziegler A. Horváth

Publication Name: Astronomy and Astrophysics

Publication Date: 1999-12-01

Volume: 349

Issue: 2

Page Range: 595-604

Description:

The interaction of shock fronts with molecular clouds is investigated. For this purpose, a two-fluid model describing an H-H2 gas mixture is applied. The resulting equations are solved with a 2D axial-symmetric, fully compressive hydrodynamics code. Radiative cooling and the thermodynamical properties of the H2 molecule, ie. rotational and vibrational degrees of freedom as well as thermal dissociation, are taken into account. The evolution of the shock/cloud system using this more sophisticated thermodynamical model is found to be very different from that involving a pure atomic H gas which obeys the ideal gas law. For example, the maximum density of the shocked cloud is about 5-10 times lower in the latter case. This significant result might become very important when estimating triggered star formation rates. Another difference is that in the case of H-H2 mixture, the shocked cloud gets a comet-like structure because of a smaller reexpansion. From the numerical experiments we conclude that the application of the ideal gas law is insufficient and gives only a crude approximation of the real dynamics of a shock/cloud collision.

Open Access: Yes

DOI: DOI not available

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

Multigrid technique for biharmonic interpolation with application to dual and multiple reciprocity method

Csaba Gáspár

Publication Name: Numerical Algorithms

Publication Date: 1999-01-01

Volume: 21

Issue: 1-4

Page Range: 165-183

Description:

A biharmonic-type interpolation method is presented to solve 2D and 3D scattered data interpolation problems. Unlike the methods based on radial basis functions, which produce a large linear system of equations with fully populated and often non-selfadjoint and ill-conditioned matrix, the presented method converts the interpolation problem to the solution of the biharmonic equation supplied with some non-usual boundary conditions at the interpolation points. To solve the biharmonic equation, fast multigrid techniques can be applied which are based on a non-uniform, non-equidistant but Cartesian grid generated by the quadtree/octtree algorithm. The biharmonic interpolation technique is applied to the multiple and dual reciprocity method of the BEM to convert domain integrals to the boundary. This makes it possible to significantly reduce the computational cost of the evaluation of the appearing domain integrals as well as the memory requirement of the procedure. The resulting method can be considered as a special grid-free technique, since it requires no domain discretisation.

Open Access: Yes

DOI: 10.1023/a:1019173816678

The effect of the matrix condition number on the estimate of core barrel motion

M. Berta G. Pór

Publication Name: Progress in Nuclear Energy

Publication Date: 1999-01-01

Volume: 34

Issue: 1

Page Range: 1-11

Description:

It is shown, that the matrix condition number plays determining role in the error of estimation of core barrel motion when using the well known spectral decomposition methods. Matrix condition numbers were estimated for different type of reactors and detector arrangements. It is shown that in unfortunate case the statistical error of estimate can reach hundreds of the original statistical error. It is suggested to eliminate one of the freedom of the system, before making spectral decomposition, which can drastically improve the accuracy of the decomposition. © 1998 Elsevier Science Ltd. All rights reserved.

Open Access: Yes

DOI: 10.1016/s0149-1970(97)00110-8

Hausdorff dimension of univoque sets

Gábor Kallós

Publication Name: Acta Cybernetica

Publication Date: 1999-01-01

Volume: 14

Issue: 2

Page Range: 303-314

Description:

In this paper we present the results obtained so far for the determination of the Hausdorff dimension of the univoque set, in number systems with base number greater than 1. The investigation is based on the methods presented in [1] and [2]. We illustrate the theoretical results with interesting examples.

Open Access: Yes

DOI: DOI not available