Displaying similar documents to “On the convergence of the backward Euler algorithm for the multidimensional heat equation”

A domain splitting method for heat conduction problems in composite materials

Friedrich Karl Hebeker (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of fibres embedded into some standard material. For ease of presentation we consider the case of two space dimensions only. The set of finite element equations obtained by the backward Euler scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually...

Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation

Minh-Binh Tran (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz...

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Yao-Chuang Han, Yu-Feng Nie, Zhan-Bin Yuan (2019)

Applications of Mathematics

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This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision...

Heating source localization in a reduced time

Sara Beddiaf, Laurent Autrique, Laetitia Perez, Jean-Claude Jolly (2016)

International Journal of Applied Mathematics and Computer Science

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Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced....

Model of shell metal mould heating in the automotive industry

Jaroslav Mlýnek, Roman Knobloch (2018)

Applications of Mathematics

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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...