Analytical transformation of volume integral for the time-stepping BEM analysis of 2D transient heat conduction in anisotropic media.

*(English)*Zbl 1403.80027Summary: Despite the extensive study of the transient heat conduction analysis for isotropic media by the boundary element method (BEM), its relevant researches in transient heat conduction in anisotropic media still remain relatively scarce indeed. In the time-stepping BEM scheme for the transient heat conduction, the transient effect reveals itself as an additional volume integral that conventionally requires domain discretization for direct integration. However, such domain discretization will destroy the BEMs most distinctive nature that only the boundary needs to be discretized. In this paper, the domain integral is analytically transformed to the boundary so that the BEMs nature of boundary discretization is completely restored. Moreover, the domain mapping technique is combined with this transformed time-stepping scheme to treat the 2D transient heat conduction in anisotropic media. Without any internal treatments or special approximations like in other schemes, the transformed time-stepping scheme can be applied to effectively solve the problem of transient heat conduction in anisotropic media.

##### MSC:

80M15 | Boundary element methods applied to problems in thermodynamics and heat transfer |

65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

##### Keywords:

boundary element method; 2D transient anisotropic heat conduction; time-stepping boundary integral equation; domain mapping
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\textit{Y. C. Shiah} et al., Eng. Anal. Bound. Elem. 64, 101--110 (2016; Zbl 1403.80027)

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