XIX Sympozjum Srodowiskowe PTZE - materialy.pdf
XIX Sympozjum Srodowiskowe PTZE - materialy.pdf XIX Sympozjum Srodowiskowe PTZE - materialy.pdf
a) b) 45 40 35 30 25 20 15 10 5 5 10 15 20 25 30 5 10 15 20 25 30 XIX Sympozjum PTZE, Worliny 2009 Rys. 1. Badany obiekt (typu „T”): a) obiekt i jego obraz symulacyjny b) profil tomograficzny 10 2 10 0 10 -2 0 0 20 0 400 60 0 800 1000 1200 140 9 8 7 6 5 4 3 2 1 0 35 30 25 20 15 10 5 0 0 Rys. 2. Residualna norma wektora reszt w funkcji normy wektora rozwiązań (oś Y liniowa i logarytmiczna) Reprezentacja logarytmiczna pokazuje osiągnięcie prawidłowego rozwiązania, które znajduje się na pionowym załamaniu wykresu. Literatura 10 0 200 40 0 600 80 0 10 00 1 200 -4 [1] Kak A., C., Slaney M.: Principles of Computerized Tomographic Imaging, IEEE Press, 1999 [2] Lawson C. L., Hanson R. J.: Solving Least Squares Problems”, Classics in Applied Mathematics 15, SIAM, 1995 [3] Polakowski K., Filipowicz F.S., Filipowicz Z.: 2,5D tomographic imaging for ultrasonic investigations, Przegląd Elektrotechniczny, nr 2, 2007, pp. 113-115 [4] Polakowski K., Sikora J., Filipowicz F.S.: SVD for image construction in ultrasound tomography, The International Conference on “Computer as a Tool” EUROCON, Warszawa, 2007, pp. 276-281 [5] Polakowski K., Sikora J.: Visualization and image analysis problems in multipath ultrasonic tomography, 5th World Congress on Industrial Process Tomography WCIPT5, Bergen, 2007, pp. 941-948 5 10 15 20 25 30 35
XIX Sympozjum PTZE, Worliny 2009 POTENTIAL FORMULATIONS FOR SOLVING TEAM PROBLEM 27 Zoltán Pólik, Miklós Kuczmann Laboratory of Electromagnetic Fields, Széchenyi István University, H-9026, Egyetem tér 1, Győr, Hungary e-mail: polikzoltan@gmail.com In the case of many applications, for example NDT and NDE systems, but the most devices based on electromagnetic discipline, the exact modelling is very important during the development stage. The problem 27 of TEAM Workshops provides experimental and numerical solutions of a known problem [1]. It is a useful example to test the efficiency and the speed of different numerical methods. The built up of the arrangement can be seen in Fig. 1, which is implemented in the frame of the COMSOL Multiphysics software package. Fig. 1. The finite element mesh of the arrangement Above an aluminum cylinder there are a „pancake coil” and two sensors which are able to measure the horizontal radial component of the magnetic flux density. Below one of the sensors there can be three different flaws. The measured quantity – HDFD (Horizontal Differential Flux Density) – is the difference between the tensions provided by the two sensors during a current turn-off effect [2]. The simulated results of the problem by the International TEAM Workshop can be seen in Fig. 2. In the present, a three dimensional finite element model has been built up to simulate the HDFD of the above arrangement in the case of the three defined flaws by using the A,V – A potential formulation with vector finite elements [3,4]. 141
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<strong>XIX</strong> <strong>Sympozjum</strong> <strong>PTZE</strong>, Worliny 2009<br />
POTENTIAL FORMULATIONS<br />
FOR SOLVING TEAM PROBLEM 27<br />
Zoltán Pólik, Miklós Kuczmann<br />
Laboratory of Electromagnetic Fields,<br />
Széchenyi István University, H-9026, Egyetem tér 1, Győr, Hungary<br />
e-mail: polikzoltan@gmail.com<br />
In the case of many applications, for example NDT and NDE systems, but the most devices<br />
based on electromagnetic discipline, the exact modelling is very important during the<br />
development stage.<br />
The problem 27 of TEAM Workshops provides experimental and numerical solutions of a<br />
known problem [1]. It is a useful example to test the efficiency and the speed of different<br />
numerical methods.<br />
The built up of the arrangement can be seen in Fig. 1, which is implemented in the frame of<br />
the COMSOL Multiphysics software package.<br />
Fig. 1. The finite element mesh of the arrangement<br />
Above an aluminum cylinder there are a „pancake coil” and two sensors which are able to<br />
measure the horizontal radial component of the magnetic flux density. Below one of the<br />
sensors there can be three different flaws. The measured quantity – HDFD (Horizontal<br />
Differential Flux Density) – is the difference between the tensions provided by the two<br />
sensors during a current turn-off effect [2]. The simulated results of the problem by the<br />
International TEAM Workshop can be seen in Fig. 2.<br />
In the present, a three dimensional finite element model has been built up to simulate the<br />
HDFD of the above arrangement in the case of the three defined flaws by using the A,V – A<br />
potential formulation with vector finite elements [3,4].<br />
141