Partial dimension reduction for the heat equation in a domain containing thin tubes

Abstract

The heat equation in considered in a domain containing thin cylindrical tubes with Neumann's boundary condition at the lateral boundary of these tubes. This problem is reduced to a hybrid dimension problem keeping the initial dimension out of thin tubes and reducing it to the one-dimensional heat equation within the tubes at some distance from the bases of the cylinders. Junction of models of different dimensions is done according to the method of asymptotic partial decomposition of domain. The difference of solutions of the original and partially reduced problems is estimated. This result generalizes the method of partial dimension reduction for the case when the domain has only one restriction that it contains several thin cylinders possibly of different orders of diameters. KEYWORDS asymptotic partial decomposition of domain, dimension reduction, domain containing thin tubes, estimates of the error, heat equation Math Meth Appl Sci. 2018;41:9529-9545.wileyonlinelibrary.com/journal/mma

Parallel 3D ADI Scheme for Partially Dimension Reduced Heat Conduction Problem

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Partial Decomposition of a Domain Containing Thin Tubes for Solving the Diffusion Equation

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Asymptotic Domain Decomposition Method for Approximation the Spectrum of the Diffusion Operator in a Domain Containing Thin Tubes

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