COUPLING BOUNDARY ELEMENT METHOD WITH LEVEL SET METHOD TO SOLVE INVERSE PROBLEM
Tomasz Rymarczyk
tomasz.rymarczyk@netrix.com.plNetrix S.A., Research and Development Center (Poland)
Paweł Tchórzewski
Netrix S.A., Research and Development Center (Poland)
Jan Sikora
Lublin University of Technology, Institute of Electronics and Information Technology; Electrotechnical Institute (Poland)
Abstract
The boundary element method and the level set method can be used in order to solve the inverse problem for electric field. In this approach the adjoint equation arises in each iteration step. Results of the numerical calculations show that the boundary element method can be applied successfully to obtain approximate solution of the adjoint equation. The proposed solution algorithm is initialized by using topological sensitivity analysis. Shape derivatives and material derivatives have been incorporated with the level set method to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations. The coupled algorithm is a relatively new procedure to overcome this problem. Experimental results have demonstrated the efficiency of the proposed approach to achieve the solution of the inverse problem.
Keywords:
inverse problem, boundary element method, level set methodReferences
Allaire G., Gournay F. De, Jouve F., Toader A. M.: Structural optimization using topological and shape sensitivity via a level set method, Control and Cybernetics, vol. 34, 2005, 59–80.
Google Scholar
Chen W., Cheng J., Lin W.: A level set method to reconstruct the discontinuity of the conductivity in EIT, Science in China Series A: Mathematics, vol. 52, 2009.
Google Scholar
Ito K., Kunish K., Li Z.: The Level-Set Function Approach to an Inverse Interface Problem, Inverse Problems, vol. 17, no. 5, 2001, 1225–1242.
Google Scholar
Jabłoński P.: Metoda elementów brzegowych w analizie pola elektromagnetycznego, Wydawnictwo Politechniki Częstochowskiej, 2003.
Google Scholar
Osher S., Sethian J. A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics, vol. 79, 1988, 12–49.
Google Scholar
Osher S., Santosa F.: Level set methods for optimization problems involving geometry and constraints. Frequencies of a two-density inhomogeneous drum, Journal of Computational Physics, vol. 171, 2001, 272–288.
Google Scholar
Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces, Springer New York, 2003.
Google Scholar
Rymarczyk T.: Using electrical impedance tomography to monitoring flood banks, International Journal of Applied Electromagnetics and Mechanics 45, 2014, 489–494.
Google Scholar
Rymarczyk T.: Characterization of the shape of unknown objects by inverse numerical methods, Przegląd Elektrotechniczny, R. 88, 7b, 2012, 138-140.
Google Scholar
Rymarczyk T., Sikora J., Waleska B.: Coupled Boundary Element Method and Level Set Function for Solving Inverse Problem in EIT, 7th World Congress on Industrial Process Tomography, WCIPT7, Krakow 2013.
Google Scholar
Rymarczyk:T., Adamkiewicz P., Duda K., Szumowski J., Sikora J.: New Electrical Tomographic Method to Determine Dampness in Historical Buildings, Achieve of Electrical Engineering, v.65, 2/2016, 273–283
Google Scholar
Sethian J.A.: Level Set Methods and Fast Marching Methods, Cambridge Univeristy Press, 1999.
Google Scholar
Sikora J.: Boundary Element Method for Impedance and Optical Tomography, Warsaw University of Technology Publisher, 2007.
Google Scholar
Smolik W, Forward Problem Solver for Image Reconstruction by Nonlinear Optimization in Electrical Capacitance Tomography, Flow Measurement and Instrumentation, Vol. 21, Issue 1, 2010, 70–77.
Google Scholar
Wajman R., Fiderek P., Fidos H., Jaworski T., Nowakowski J., Sankowski D., Banasiak R.: Metrological evaluation of a 3D electrical capacitance tomography measurement system for two-phase flow fraction determination; Meas. Sci. Technol. Vol. 24, 2013, No. 065302.
Google Scholar
Tai C., Chung E., Chan T.: Electrical impedance tomography using level set representation and total variational regularization, Journal of Computational Physics, vol. 205, no. 1, 2005, 357–372.
Google Scholar
Vese L., Chan T.: A new multiphase level set framework for image segmentation via the Mumford and Shah model. CAM Report 01-25, UCLA Math. Dept., 2001.
Google Scholar
Authors
Tomasz Rymarczyktomasz.rymarczyk@netrix.com.pl
Netrix S.A., Research and Development Center Poland
Authors
Paweł TchórzewskiNetrix S.A., Research and Development Center Poland
Authors
Jan SikoraLublin University of Technology, Institute of Electronics and Information Technology; Electrotechnical Institute Poland
Statistics
Abstract views: 258PDF downloads: 65
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Most read articles by the same author(s)
- Grzegorz Kłosowski, Tomasz Rymarczyk, USING NEURAL NETWORKS AND DEEP LEARNING ALGORITHMS IN ELECTRICAL IMPEDANCE TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 3 (2017)
- Tomasz Rymarczyk, Tomasz Cieplak, Grzegorz Kłosowski, Paweł Rymarczyk, DESIGN OF DATA ANALYSIS SYSTEMS FOR BUSINESS PROCESS AUTOMATION , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 3 (2018)
- Tomasz Rymarczyk, Michał Gołąbek, Piotr Lesiak, Andrzej Marciniak, Mirosław Guzik, CONSTRUCTION OF AN ULTRASONIC TOMOGRAPH FOR ANALYSIS OF TECHNOLOGICAL PROCESSES IN THE FIELD OF REFLECTION AND TRANSMISSION WAVES , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Tomasz Rymarczyk, Grzegorz Kłosowski, THE USE OF ARTIFICIAL INTELLIGENCE IN AUTOMATED IN-HOUSE LOGISTICS CENTRES , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 1 (2018)
- Tomasz Rymarczyk, Bartek Przysucha, Marcin Kowalski, Piotr Bednarczuk, ANALYSIS OF DATA FROM MEASURING SENSORS FOR PREDICTION IN PRODUCTION PROCESS CONTROL SYSTEMS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Tomasz Rymarczyk, Krzysztof Polakowski, Jan Sikora, A NEW CONCEPT OF DISCRETIZATION MODEL FOR IMAGING IMPROVING IN ULTRASOUND TRANSMISSION TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 9 No. 4 (2019)
- Konrad Niderla, Tomasz Rymarczyk, Jan Sikora, MANUFACTURING PLANNING AND CONTROL SYSTEM USING TOMOGRAPHIC SENSORS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 3 (2018)
- Tomasz Rymarczyk, Jan Sikora, SINGULAR INTEGRATION IN BOUNDARY ELEMENT METHOD FOR HELMHOLTZ EQUATION FORMULATED IN FREQUENCY DOMAIN , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 11 No. 4 (2021)
- Tomasz Rymarczyk, Jan Sikora, SOME MORE ON LOGARITHMIC SINGULARITY INTEGRATION IN BOUNDARY ELEMENT METOD , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 14 No. 1 (2024)
- Grzegorz Kłosowski, Tomasz Rymarczyk, APPLICATION OF CONVOLUTIONAL NEURAL NETWORKS IN WALL MOISTURE IDENTIFICATION BY EIT METHOD , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 12 No. 1 (2022)