A Splitting Scheme for Diffusion and Heat Conduction Problems

Gladky, A. V.; Gladka, Yuliya

doi:10.1007/s10559-019-00209-5

Cited by 2 publications

(1 citation statement)

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“…Optimization methods are widely used to solve direct problems of heat conduction. Gladky and Gladka [25] considered the problem of mathematical modelling and optimization of non-stationary diffusion and heat-conducting processes. For the numerical solution of multidimensional initial-boundary value problems of diffusion and heat conduction, an approach was proposed that uses the idea of splitting and calculating the obtained difference schemes employing explicit schemes of point calculations.…”

Section: Introductionmentioning

confidence: 99%

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

Krysko

Awrejcewicz

Bodyagina³

et al. 2021

Mathematics and Mechanics of Solids

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We propose applying topological optimization methods based on measuring temperature and heat fluxes to estimate the thermal conductivity of inhomogeneous thermally conductive plates and determine the shape and location of foreign inclusions. Examples of plates subjected to external heat fluxes and heat sources are considered. The solutions are obtained with the help of the finite element method combined with the method of moving asymptotes. The results show that identification accuracy depends on the defined boundary conditions, the source intensity value, heat fluxes, temperature distribution and the shape of the inclusions. For the problem of 18 circular inclusions under different heat fluxes, identification accuracy increases with increasing source intensity values.

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Section: Introductionmentioning

confidence: 99%