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Dr. David Pánek
Department of Theory of Electrical Engineering, University of West Bohemia, 30614 Pilsen, Czech Republic.

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Research Keywords & Expertise

0 Electrical Machines
0 Modeling
0 Numerical Analysis
0 Optimization
0 applied and computational mathematics

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Optimization
Modeling
Robust design optimization
Electrical Machines
Numerical Analysis

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Review
Published: 23 September 2020 in Applied Sciences
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The bio-inspired algorithms are novel, modern, and efficient tools for the design of electrical machines. However, from the mathematical point of view, these problems belong to the most general branch of non-linear optimization problems, where these tools cannot guarantee that a global minimum is found. The numerical cost and the accuracy of these algorithms depend on the initialization of their internal parameters, which may themselves be the subject of parameter tuning according to the application. In practice, these optimization problems are even more challenging, because engineers are looking for robust designs, which are not sensitive to the tolerances and the manufacturing uncertainties. These criteria further increase these computationally expensive problems due to the additional evaluations of the goal function. The goal of this paper is to give an overview of the widely used optimization techniques in electrical machinery and to summarize the challenges and open problems in the applications of the robust design optimization and the prospects in the case of the newly emerging technologies.

ACS Style

Tamás Orosz; Anton Rassõlkin; Ants Kallaste; Pedro Arsénio; David Pánek; Jan Kaska; Pavel Karban. Robust Design Optimization and Emerging Technologies for Electrical Machines: Challenges and Open Problems. Applied Sciences 2020, 10, 6653 .

AMA Style

Tamás Orosz, Anton Rassõlkin, Ants Kallaste, Pedro Arsénio, David Pánek, Jan Kaska, Pavel Karban. Robust Design Optimization and Emerging Technologies for Electrical Machines: Challenges and Open Problems. Applied Sciences. 2020; 10 (19):6653.

Chicago/Turabian Style

Tamás Orosz; Anton Rassõlkin; Ants Kallaste; Pedro Arsénio; David Pánek; Jan Kaska; Pavel Karban. 2020. "Robust Design Optimization and Emerging Technologies for Electrical Machines: Challenges and Open Problems." Applied Sciences 10, no. 19: 6653.

Journal article
Published: 06 March 2020 in Computers & Mathematics with Applications
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Two powerful and versatile code packages (Agros Suite and Ārtap) are presented for design and optimization of technical devices and systems. Agros Suite represents an environment for numerical solution of systems consisting of partial differential equations (PDEs) of the second order by a higher-order finite element method with a lot of further advanced features such as full adaptivity and selected optimization techniques. Ārtap is a robust design optimization toolbox that provides a simple and efficient programming environment for a wide-range of optimization methods, integrated and external PDE solvers and well-established machine learning tools. Both packages are described in a sufficient detail and their power is illustrated with solution of three problems from the domain of technical sciences.

ACS Style

Pavel Karban; David Pánek; Tamás Orosz; Iveta Petrášová; Ivo Doležel. FEM based robust design optimization with Agros and Ārtap. Computers & Mathematics with Applications 2020, 81, 618 -633.

AMA Style

Pavel Karban, David Pánek, Tamás Orosz, Iveta Petrášová, Ivo Doležel. FEM based robust design optimization with Agros and Ārtap. Computers & Mathematics with Applications. 2020; 81 ():618-633.

Chicago/Turabian Style

Pavel Karban; David Pánek; Tamás Orosz; Iveta Petrášová; Ivo Doležel. 2020. "FEM based robust design optimization with Agros and Ārtap." Computers & Mathematics with Applications 81, no. : 618-633.

Journal article
Published: 17 February 2020 in Applied Sciences
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Since large power transformers are custom-made, and their design process is a labor-intensive task, their design process is split into different parts. In tendering, the price calculation is based on the preliminary design of the transformer. Due to the complexity of this task, it belongs to the most general branch of discrete, non-linear mathematical optimization problems. Most of the published algorithms are using a copper filling factor based winding model to calculate the main dimensions of the transformer during this first, preliminary design step. Therefore, these cost optimization methods are not considering the detailed winding layout and the conductor dimensions. However, the knowledge of the exact conductor dimensions is essential to calculate the thermal behaviour of the windings and make a more accurate stray loss calculation. The paper presents a novel, evolutionary algorithm-based transformer optimization method which can determine the optimal conductor shape for the windings during this examined preliminary design stage. The accuracy of the presented FEM method was tested on an existing transformer design. Then the results of the proposed optimization method have been compared with a validated transformer design optimization algorithm.

ACS Style

Tamás Orosz; David Pánek; Pavel Karban. FEM Based Preliminary Design Optimization in Case of Large Power Transformers. Applied Sciences 2020, 10, 1361 .

AMA Style

Tamás Orosz, David Pánek, Pavel Karban. FEM Based Preliminary Design Optimization in Case of Large Power Transformers. Applied Sciences. 2020; 10 (4):1361.

Chicago/Turabian Style

Tamás Orosz; David Pánek; Pavel Karban. 2020. "FEM Based Preliminary Design Optimization in Case of Large Power Transformers." Applied Sciences 10, no. 4: 1361.

Preprint
Published: 31 December 2019
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Since large power transformers are custom-made, and their design process is a labor-intensive task, their design process is split into different parts. In tendering, the price calculation is based on the preliminary design of the transformer. Due to the complexity of this task, it belongs to the most general branch of discrete, non-linear mathematical optimization problems. Most of the published algorithms are using a copper filling factor based winding model to calculate the main dimensions of the transformer during this first, preliminary design step. Therefore, these cost optimization methods are not considering the detailed winding layout and the conductor dimensions. However, the knowledge of the exact conductor dimensions is essential to calculate the thermal behaviour of the windings and make a more accurate stray loss calculation. The paper presents a novel, evolutionary algorithm-based transformer optimization method which can determine the optimal conductor shape for the windings during this examined preliminary design stage. The accuracy of the presented FEM method was tested on an existing transformer design. Then the results of the proposed optimization method have been compared with a validated transformer design optimization algorithm.

ACS Style

Tamás Orosz; David Pánek; Pavel Karban. FEM Based Preliminary Design Optimization in Case of Large Power Transformers. 2019, 1 .

AMA Style

Tamás Orosz, David Pánek, Pavel Karban. FEM Based Preliminary Design Optimization in Case of Large Power Transformers. . 2019; ():1.

Chicago/Turabian Style

Tamás Orosz; David Pánek; Pavel Karban. 2019. "FEM Based Preliminary Design Optimization in Case of Large Power Transformers." , no. : 1.

Journal article
Published: 22 March 2019 in IEEE Transactions on Magnetics
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A method of finding the temperature dependences of physical parameters of metals is proposed and discussed. The method is based on the combination of measurement of the surface temperature of the material and subsequent solution of the inverse problem using the multi-parametric optimization. Particular steps and algorithms are illustrated with an example.

ACS Style

David Panek; Pavel Karban; Ivo Dolezel. Calibration of Numerical Model of Magnetic Induction Brazing. IEEE Transactions on Magnetics 2019, 55, 1 -4.

AMA Style

David Panek, Pavel Karban, Ivo Dolezel. Calibration of Numerical Model of Magnetic Induction Brazing. IEEE Transactions on Magnetics. 2019; 55 (6):1-4.

Chicago/Turabian Style

David Panek; Pavel Karban; Ivo Dolezel. 2019. "Calibration of Numerical Model of Magnetic Induction Brazing." IEEE Transactions on Magnetics 55, no. 6: 1-4.

Conference paper
Published: 01 September 2018 in 19th International Conference Computational Problems of Electrical Engineering
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The paper is divided into two parts. In the first section the paper deals with shape optimization of high-power converter busbar. The second section is focused on the topology optimization which was applied on the busbar. The main goal of the optimization is to ensure that the power is equally distributed among particular active components.

ACS Style

Iveta Petrasova; Pavel Karban; David Panek; Lenka Sroubova. Shape and Topology Optimization of High Power Converter Busbar. 19th International Conference Computational Problems of Electrical Engineering 2018, 1 -4.

AMA Style

Iveta Petrasova, Pavel Karban, David Panek, Lenka Sroubova. Shape and Topology Optimization of High Power Converter Busbar. 19th International Conference Computational Problems of Electrical Engineering. 2018; ():1-4.

Chicago/Turabian Style

Iveta Petrasova; Pavel Karban; David Panek; Lenka Sroubova. 2018. "Shape and Topology Optimization of High Power Converter Busbar." 19th International Conference Computational Problems of Electrical Engineering , no. : 1-4.

Journal article
Published: 02 July 2018 in COMPEL - The international journal for computation and mathematics in electrical and electronic engineering
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ACS Style

Pavel Karban; David Pánek; Ivo Doležel. Model of induction brazing of nonmagnetic metals using model order reduction approach. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 2018, 37, 1515 -1524.

AMA Style

Pavel Karban, David Pánek, Ivo Doležel. Model of induction brazing of nonmagnetic metals using model order reduction approach. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 2018; 37 (4):1515-1524.

Chicago/Turabian Style

Pavel Karban; David Pánek; Ivo Doležel. 2018. "Model of induction brazing of nonmagnetic metals using model order reduction approach." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4: 1515-1524.

Proceedings article
Published: 01 May 2018 in 2018 ELEKTRO
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The paper deals with calculation of iso-lines of radiation-field from isotropic rectangular source using pseudo arc-length continuation. The proposed approach is demonstrated on fire-safety application.

ACS Style

David Pánek; Pavel Karban; Ivo Dolezel; Vaclav Petras. Calculation of radiation field iso-surfaces using numerical continuation method. 2018 ELEKTRO 2018, 1 -4.

AMA Style

David Pánek, Pavel Karban, Ivo Dolezel, Vaclav Petras. Calculation of radiation field iso-surfaces using numerical continuation method. 2018 ELEKTRO. 2018; ():1-4.

Chicago/Turabian Style

David Pánek; Pavel Karban; Ivo Dolezel; Vaclav Petras. 2018. "Calculation of radiation field iso-surfaces using numerical continuation method." 2018 ELEKTRO , no. : 1-4.

Journal article
Published: 01 February 2018 in Applied Mathematics and Computation
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ACS Style

David Pánek; Václav Kotlan; Roman Hamar; Ivo Doležel. Novel algorithm for modeling combined laser and induction welding respecting keyhole effect. Applied Mathematics and Computation 2018, 319, 254 -263.

AMA Style

David Pánek, Václav Kotlan, Roman Hamar, Ivo Doležel. Novel algorithm for modeling combined laser and induction welding respecting keyhole effect. Applied Mathematics and Computation. 2018; 319 ():254-263.

Chicago/Turabian Style

David Pánek; Václav Kotlan; Roman Hamar; Ivo Doležel. 2018. "Novel algorithm for modeling combined laser and induction welding respecting keyhole effect." Applied Mathematics and Computation 319, no. : 254-263.

Journal article
Published: 29 December 2017 in Open Physics
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A model of hybrid cladding on a cylindrical surface is built and numerically solved. Heating of both substrate and the powder material to be deposited on its surface is realized by laser beam and preheating inductor. The task represents a hard-coupled electromagnetic-thermal problem with time-varying geometry. Two specific algorithms are developed to incorporate this effect into the model, driven by local distribution of temperature and its gradients. The algorithms are implemented into the COMSOL Multiphysics 5.2 code that is used for numerical computations of the task. The methodology is illustrated with a typical example whose results are discussed.

ACS Style

Václav Kotlan; Roman Hamar; David Pánek; Ivo Doležel. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process. Open Physics 2017, 15, 971 -978.

AMA Style

Václav Kotlan, Roman Hamar, David Pánek, Ivo Doležel. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process. Open Physics. 2017; 15 (1):971-978.

Chicago/Turabian Style

Václav Kotlan; Roman Hamar; David Pánek; Ivo Doležel. 2017. "Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process." Open Physics 15, no. 1: 971-978.

Journal article
Published: 31 October 2017 in IEEE Transactions on Magnetics
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A methodology of optimizing the process of combined laser cladding with induction preheating is proposed and verified. The resultant shape of the deposited layer consisting of a series of parallel tracks should be as uniform as possible and resistant with respect to cracks of any origin. The main aim is to develop a technique (based on a simple experiment) of calibrating geometrically more complex 3-D arrangements. The task consists of a solution of a strongly nonlinear coupled electromagnetic-thermal problem (forward part) and multi-parametric optimization (backward part). The solution of the forward part uses a specific h-adaptive technique developed by authors that allows working with continuously varying geometry of the system due to added powder material.

ACS Style

Vaclav Kotlan; David Panek; Roman Hamar; Ivo Dolezel. Shape Optimization of Deposited Layer Produced by Combined Cladding Process. IEEE Transactions on Magnetics 2017, 54, 1 -4.

AMA Style

Vaclav Kotlan, David Panek, Roman Hamar, Ivo Dolezel. Shape Optimization of Deposited Layer Produced by Combined Cladding Process. IEEE Transactions on Magnetics. 2017; 54 (3):1-4.

Chicago/Turabian Style

Vaclav Kotlan; David Panek; Roman Hamar; Ivo Dolezel. 2017. "Shape Optimization of Deposited Layer Produced by Combined Cladding Process." IEEE Transactions on Magnetics 54, no. 3: 1-4.

Journal article
Published: 09 October 2017 in IEEE Transactions on Magnetics
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This paper presents a new technique of shape optimization of devices taking into account acceptable tolerances of their dimensions. The technique is based on a combination of classic optimization procedures and a sensitivity analysis carried out in several steps in the course of the optimization process. This analysis is able to decide whether the given variant is worth further optimizing or the changes in the objective functions are unacceptably high even with small variations of parameters (such a variant is immediately rejected). The power of the methodology is illustrated on an example of induction brazing, whose results are discussed.

ACS Style

David Panek; Roman Hamar; Ivo Dolezel. Shape Optimization of Devices Taking Into Account Production Tolerances. IEEE Transactions on Magnetics 2017, 54, 1 -4.

AMA Style

David Panek, Roman Hamar, Ivo Dolezel. Shape Optimization of Devices Taking Into Account Production Tolerances. IEEE Transactions on Magnetics. 2017; 54 (3):1-4.

Chicago/Turabian Style

David Panek; Roman Hamar; Ivo Dolezel. 2017. "Shape Optimization of Devices Taking Into Account Production Tolerances." IEEE Transactions on Magnetics 54, no. 3: 1-4.

Journal article
Published: 01 September 2017 in Journal of Electrical Engineering
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A new approach to estimation of unknown material parameters and boundary conditions of physical models was developed. The approach is based on processing measured data by advanced optimization techniques connected with penalization. The data are supposed to be in the form of random variables with normal probability distributions. Several examples were calculated proving the strength of the proposed algorithm.

ACS Style

Pavel Karban; David Pánek; František Mach; Ivo Doležel. Calibration of numerical models based on advanced optimization and penalization techniques. Journal of Electrical Engineering 2017, 68, 396 -400.

AMA Style

Pavel Karban, David Pánek, František Mach, Ivo Doležel. Calibration of numerical models based on advanced optimization and penalization techniques. Journal of Electrical Engineering. 2017; 68 (5):396-400.

Chicago/Turabian Style

Pavel Karban; David Pánek; František Mach; Ivo Doležel. 2017. "Calibration of numerical models based on advanced optimization and penalization techniques." Journal of Electrical Engineering 68, no. 5: 396-400.

Journal article
Published: 06 March 2017 in COMPEL - The international journal for computation and mathematics in electrical and electronic engineering
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Purpose This paper aims to present a methodology of finding temperature dependencies of selected physical parameters of metals. The method is based on the combination of measurement of the surface temperature of material during the process of heating and subsequent solution of the inverse problem using multi-parametric optimization. Design/methodology/approach The methodology is based on measurements and numerical solution of the forward and inverse problem, taking into account all involved nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). The inverse problem is solved by a genetic algorithm. Findings The suggested methodology was successfully verified on several metal materials whose temperature-dependent parameters are known. The calculated and measured results exhibit a very good accordance (the differences do not exceed about 10 per cent for room and higher temperatures). Research limitations/implications At this moment, the methodology successfully works when the temperature dependence of just one material parameter is to be found (which means that the temperature dependencies of other parameters are known). The accuracy of results also depends on the correctness of other input data. Practical implications This paper provides a relatively easy possibility of finding the temperature dependencies of thermal conductivity or heat capacity of various alloys. Originality/value The paper proposes a methodology of finding the temperature dependence of a given material parameter that is not known in advance (which is of great importance in case of alloys).

ACS Style

David Pánek; Václav Kotlan; Roman Hamar; Ivo Doležel. Inverse technique for determining temperature dependence of material properties. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 2017, 36, 427 -435.

AMA Style

David Pánek, Václav Kotlan, Roman Hamar, Ivo Doležel. Inverse technique for determining temperature dependence of material properties. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 2017; 36 (2):427-435.

Chicago/Turabian Style

David Pánek; Václav Kotlan; Roman Hamar; Ivo Doležel. 2017. "Inverse technique for determining temperature dependence of material properties." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 2: 427-435.

Journal article
Published: 06 March 2017 in COMPEL - The international journal for computation and mathematics in electrical and electronic engineering
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Purpose This paper aims to present a three-dimensional (3D) model of hybrid laser welding of a steel plate. Before welding, the plate is pre- and/or post-heated by induction to avoid mechanical stresses in material due to high gradients of temperature. Welding itself is realized by laser beam without welding rod. The model takes into account existence of both solid and liquid phases in the weld. Design/methodology/approach Presented is the complete mathematical model of the above heat treatment process, taking into account all relevant nonlinearities (saturation curve of the processed steel material and temperature dependences of its physical parameters). Its numerical solution is realized by the finite element method. Some important results are compared with experimental data. Findings In comparison with the former model developed by the authors that did not take into account the phase change, the results are more realistic and exhibit a better accordance with measurements. On the other hand, they strongly depend on sufficiently accurate knowledge of material parameters in both solid and liquid levels (that represent the input data). Research limitations/implications The quality of calculated results strongly depends on the material properties and their temperature dependencies. In case of alloys (whose chemical composition may vary in some range), such data are often unavailable and must be estimated on the basis of experiments. Another quantity that has to be calibrated is the time dependence of power delivered by the laser beam, which is due to the production of a plasma cloud above the exposed spot. Practical implications The presented model and methodology of its solution may represent a basis for design of the complete technology of laser welding with induction pre-heating and/or post-heating. Originality/value Fully 3D model of hybrid laser welding (supplemented with pre- and/or post-heating by magnetic induction) taking into account both solid and liquid phases of welded metal and influence of the plasma cloud is presented.

ACS Style

Ivo Doležel; Václav Kotlan; Roman Hamar; David Pánek. Numerical modeling of hybrid laser welding taking into account phase change of material. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 2017, 36, 417 -426.

AMA Style

Ivo Doležel, Václav Kotlan, Roman Hamar, David Pánek. Numerical modeling of hybrid laser welding taking into account phase change of material. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 2017; 36 (2):417-426.

Chicago/Turabian Style

Ivo Doležel; Václav Kotlan; Roman Hamar; David Pánek. 2017. "Numerical modeling of hybrid laser welding taking into account phase change of material." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 2: 417-426.

Conference paper
Published: 01 November 2016 in 2016 IEEE Conference on Electromagnetic Field Computation (CEFC)
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A novel way of calibration (estimation of unknown material parameters and boundary conditions) of physical models is presented, based on measured data and advanced optimization and penalization techniques. The methodology is illustrated with an example whose results are discussed.

ACS Style

David Pánek; Pavel Karban; František Mach; Dolezel Ivo. Utilization of advanced optimization and penalization techniques for calibration of numerical models. 2016 IEEE Conference on Electromagnetic Field Computation (CEFC) 2016, 1 -1.

AMA Style

David Pánek, Pavel Karban, František Mach, Dolezel Ivo. Utilization of advanced optimization and penalization techniques for calibration of numerical models. 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). 2016; ():1-1.

Chicago/Turabian Style

David Pánek; Pavel Karban; František Mach; Dolezel Ivo. 2016. "Utilization of advanced optimization and penalization techniques for calibration of numerical models." 2016 IEEE Conference on Electromagnetic Field Computation (CEFC) , no. : 1-1.

Conference paper
Published: 01 November 2016 in 2016 IEEE Conference on Electromagnetic Field Computation (CEFC)
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Novel approach to modeling of 3D coupled electroheat problems with time-varying geometries is presented. Instead of time-expensive remeshing of the whole system in every time step it is used the initial mesh that takes into account the expected geometric changes. In the course of computations, its relevant elements are able to adaptively change their shapes and material parameters. The methodology is illustrated with an example of combined cladding.

ACS Style

Vaclav Kotlan; Ivo Dolezel; Roman Hamar; David Panek. Modeling of selected 3D electroheat coupled problems with time-varying geometries. 2016 IEEE Conference on Electromagnetic Field Computation (CEFC) 2016, 1 -1.

AMA Style

Vaclav Kotlan, Ivo Dolezel, Roman Hamar, David Panek. Modeling of selected 3D electroheat coupled problems with time-varying geometries. 2016 IEEE Conference on Electromagnetic Field Computation (CEFC). 2016; ():1-1.

Chicago/Turabian Style

Vaclav Kotlan; Ivo Dolezel; Roman Hamar; David Panek. 2016. "Modeling of selected 3D electroheat coupled problems with time-varying geometries." 2016 IEEE Conference on Electromagnetic Field Computation (CEFC) , no. : 1-1.

Conference paper
Published: 01 September 2016 in 2016 17th International Conference Computational Problems of Electrical Engineering (CPEE)
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A 3D model of combined induction and laser cladding is presented. This electroheat process is characterized by time-varying geometry because of material added in the form of metal powder in order to form the clad. The paper brings a novel approach to its modeling which required expensive remeshing of the whole investigated domain in every time step. The offered technique is based on local adaptive refinement of the existing mesh that allows detailed mapping of distribution of temperature in the thermally exposed domain and assigning the correct parameters of the present material. In this way it is possible to distinguish both solid and liquid phases and also (after cooling and solidification) the final shape of the clad that is not known in advance. The methodology is illustrated with a typical example whose results are discussed.

ACS Style

Vaclav Kotlan; David Pánek; Roman Hamar; Ivo Dolezel. Combination of induction and laser cladding and its 3D computer model. 2016 17th International Conference Computational Problems of Electrical Engineering (CPEE) 2016, 1 -4.

AMA Style

Vaclav Kotlan, David Pánek, Roman Hamar, Ivo Dolezel. Combination of induction and laser cladding and its 3D computer model. 2016 17th International Conference Computational Problems of Electrical Engineering (CPEE). 2016; ():1-4.

Chicago/Turabian Style

Vaclav Kotlan; David Pánek; Roman Hamar; Ivo Dolezel. 2016. "Combination of induction and laser cladding and its 3D computer model." 2016 17th International Conference Computational Problems of Electrical Engineering (CPEE) , no. : 1-4.

Journal article
Published: 04 July 2016 in COMPEL - The international journal for computation and mathematics in electrical and electronic engineering
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Purpose – The purpose of this paper is to propose and analyze a combined heat treatment of metal materials, consisting in classic induction pre-heating and/or post-heating and full heating by laser beam. This technology is prospective for some kinds of surface hardening and welding because its application leads to lowering of temperature gradients at the heated spots, which substantially reduces local residual mechanical strains and stresses. Design/methodology/approach – The task was solved like the 3D hard-coupled problem for electromagnetic field, temperature field and field of displacements. It was solved numerically using the techniques based on the FEM. For solution was used commercial software COMSOL Multiphysics, some parts were solved using own scripts in the software Agros. Findings – In the paper are shown results of the numerical solution and experimental measured data. Due the work the authors found that the influence of the pre-heating and post-heating really leads to limit the temperature gradients and from other measurements is clear that also to improving of the welding. Originality/value – The paper presents fully 3D nonlinear and nonstationary mathematical model of hybrid laser welding, its numerical solution experimental verification.

ACS Style

Václav Kotlan; Roman Hamar; David Pánek; Ivo Doležel. Combined heat treatment of metal materials. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 2016, 35, 1450 -1459.

AMA Style

Václav Kotlan, Roman Hamar, David Pánek, Ivo Doležel. Combined heat treatment of metal materials. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 2016; 35 (4):1450-1459.

Chicago/Turabian Style

Václav Kotlan; Roman Hamar; David Pánek; Ivo Doležel. 2016. "Combined heat treatment of metal materials." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 4: 1450-1459.

Conference paper
Published: 01 May 2016 in 2016 ELEKTRO
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Comparison of open-source libraries for solving systems of algebraic equations is carried out. Attention is paid mainly to solvers (or preconditioners) using the method called algebraic multigrid. For comparison, several direct and iterative solvers were chosen, such as MUMPS, UMFPACK, TRILINOS, PARALUTION and PETSc. Utilization of these packages is shown on two examples.

ACS Style

Pavel Karban; David Pánek; Petr Kropik. Utilization of algebraic multigrid for solving electromagnetic field by HP-FEM. 2016 ELEKTRO 2016, 527 -532.

AMA Style

Pavel Karban, David Pánek, Petr Kropik. Utilization of algebraic multigrid for solving electromagnetic field by HP-FEM. 2016 ELEKTRO. 2016; ():527-532.

Chicago/Turabian Style

Pavel Karban; David Pánek; Petr Kropik. 2016. "Utilization of algebraic multigrid for solving electromagnetic field by HP-FEM." 2016 ELEKTRO , no. : 527-532.