A homogenization function method for inverse heat source problems in 3D functionally graded materials

Lin Qiu, Ji Lin*, Fajie Wang, Qing Hua Qin, Chein Shan Liu

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)

    Abstract

    A simple and effective method is proposed for solving inverse heat source problems in functionally graded materials based on the homogenization function. Making use of given conditions, a homogenization function for the boundary value problem is conceived and a family of homogenization functions is further derived. Then, the superposition of homogenization functions method is developed and used for determining the heat source of the inverse problems. In this new methodology, the inverse heat source problems are directly solved by calculating a linear matrix system. Importantly, this scheme does not involve mesh generation, numerical integration, iteration, regularization and fundamental solutions, and it is easy to program and implement on the existing software. Four numerical examples defined on the cuboid domains are presented to demonstrate the accuracy and efficiency of the presented tool.

    Original languageEnglish
    Pages (from-to)923-933
    Number of pages11
    JournalApplied Mathematical Modelling
    Volume91
    DOIs
    Publication statusPublished - Mar 2021

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