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3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions

Identificadores del recurso

0378-4754

http://hdl.handle.net/10498/32742

https://doi.org/10.1016/j.matcom.2024.02.018

Procedencia

(Repositorio de Objetos de Docencia e Investigación: RODIN)

Ficha

Título:: 3D numerical simulation of an anisotropic bead type thermistor and multiplicity of solutions
Tema:: Thermistor problem; Anisotropic Sobolev space; Non-uniformly elliptic system; Finite element method; Numerical solution
Descrición:: We perform some 3D numerical experiments for the approximation of the solutions to a bead type thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix whose 𝑗�th entry is of the form|𝜕�𝑢�∕𝜕�𝑥�𝑗�|𝑝�𝑗�−2𝜕�𝑢�∕𝜕�𝑥�𝑗�,𝑢� being the temperature inside the thermistor and the exponents 𝑝�𝑗�,1 ≤ 𝑗� ≤ 3, lie in the interval (1,+∞). We first show some existence results for different notions of solutions, prove a maximum principle for each type of solution, and study certain symmetry properties for these solutions in a bead type thermistor. These properties lead us to the introduction of a symmetric solution and we show the existence of such a solution. We have developed a numerical algorithm for the computation of the numerical solutions in a bead type thermistor. This algorithm combines a fixed-point technique with a standard finite element method (FEM). Some numerical tests have shown the existence of non-symmetric solutions and this leads to multiple many solutions (at least three). We discuss the numerical results obtained for different values of the exponents 𝑝�𝑗� and the applied voltage on different meshes.
Fonte:: Mathematics and Computers in Simulation, Vol. 220, 2024, pp. 640-672
Idioma:: English
Autor/Productor:: Lahrache, Manar; Ortegón Gallego, Francisco; Rhoudaf, Mohamed
Editor:: Elservier
Otros colaboradores/productores:: Matemáticas
Dereitos:: Attribution-NonCommercial-NoDerivatives 4.0 Internacional; http://creativecommons.org/licenses/by-nc-nd/4.0/; open access
Data:: 2024-06-25T08:26:12Z; 2024-02-22
Tipo de recurso:: journal article; VoR
Formato:: application/pdf

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2. <dc:creator>Lahrache, Manar</dc:creator>
3. <dc:creator>Ortegón Gallego, Francisco</dc:creator>
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5. <dc:contributor>Matemáticas</dc:contributor>
6. <dc:subject>Thermistor problem</dc:subject>
7. <dc:subject>Anisotropic Sobolev space</dc:subject>
8. <dc:subject>Non-uniformly elliptic system</dc:subject>
9. <dc:subject>Finite element method</dc:subject>
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