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On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

Michal KřížekJaroslav Mlýnek — 1994

Banach Center Publications

The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.

Model of shell metal mould heating in the automotive industry

Jaroslav MlýnekRoman Knobloch — 2018

Applications of Mathematics

This article focuses on heat radiation intensity optimization on the surface of a shell metal mould. Such moulds are used in the automotive industry in the artificial leather production (the artificial leather is used, e.g., on car dashboards). The mould is heated by infrared heaters. After the required temperature is attained, the inner mould surface is sprinkled with special PVC powder. The powder melts and after cooling down it forms the artificial leather. A homogeneous temperature field of...

The classic differential evolution algorithm and its convergence properties

Roman KnoblochJaroslav MlýnekRadek Srb — 2017

Applications of Mathematics

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...

The box method and some error estimation

Mlýnek, Jaroslav — 2008

Programs and Algorithms of Numerical Mathematics

This article focuses its attention on practical use of the box method for solving certain type of partial differential equations. The heat conduction problem of the oil transformer under stationary load is described by this equation. The knowledge of the transformer operating temperature is important for ensuring correct functionality and lifespan of transformer. We consider an elliptic partial differential equation of second order with the Newton boundary condition on a rectangular domain. The...

The application of the thermal balance method for computation of warming in electric machines

Mlýnek, Jaroslav — 2006

Programs and Algorithms of Numerical Mathematics

The paper describes the procedure of the thermal balance method implementation for the computation of warming in electrical machines. Our effort will be focused on the temperature distribution in transformer screening under a stationary load. Since the three-dimensional problem is axially symmetric, it will be reduced by means of the cylindrical coordinates to an elliptic partial differential equation of second order with the Newton boundary conditions on a rectangular domain. Results of numerical...

Parallel programming and optimization of heat radiation intensity

Mlýnek, JaroslavSrb, Radek — 2013

Applications of Mathematics 2013

This article focuses on the practical possibilities of a suitable use of parallel programming during the computational processing of heat radiation intensity optimization across the surface of an aluminium or nickel mould. In practice, an aluminium or nickel mould is first preheated by infrared heaters located above the outer mould surface. Then the inner mould surface is sprinkled with a special PVC powder and the outer mould surface is continually warmed by infrared heaters. This is an energy-efficient...

The optimization of heat radiation intensity

Mlýnek, JaroslavSrb, Radek — 2013

Programs and Algorithms of Numerical Mathematics

This article focuses on the problem of calculating the intensity of heat radiation and its optimization across the surface of an aluminium or nickel mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. In this way artificial leathers are produced in the car industry (e.g., the artificial leather on a car dashboard). The article includes a description of how a mathematical model allows us to calculate the...

Use of a differential evolution algorithm for the optimization of the heat radiation intensity

Mlýnek, JaroslavKnobloch, RomanSrb, Radek — 2015

Application of Mathematics 2015

This article focuses on the heat radiation intensity optimization on the surface of an aluminium shell mould. The outer mould surface is heated by infrared heaters located above the mould and the inner mould surface is sprinkled with a special PVC powder. This is an economic way of producing artificial leathers in the automotive industry (e.g. the artificial leather on car dashboards). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity...

Calculation of industrial robot trajectory in frame composite production

Mlýnek, JaroslavMartinec, TomášPetrů, Michal — 2017

Programs and Algorithms of Numerical Mathematics

This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide...

The use of graphics card and nVidia CUDA architecture in the optimization of the heat radiation intensity

Mlýnek, JaroslavSrb, RadekKnobloch, Roman — 2015

Programs and Algorithms of Numerical Mathematics

The paper focuses on the acceleration of the computer optimization of heat radiation intensity on the mould surface. The mould is warmed up by infrared heaters positioned above the mould surface, and in this way artificial leathers in the automotive industry are produced (e.g. for car dashboards). The presented heating model allows us to specify the position of infrared heaters over the mould to obtain approximately even heat radiation intensity on the whole mould surface. In this way we can obtain...

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