A semi-analytical boundary collocation solver for the inverse Cauchy problems in heat conduction under 3D FGMs with heat source

Numerical Heat Transfer, Part B: Fundamentals, (online) (2019),
https://www.tandfonline.com/eprint/2M92PMSMXPX276UZMFHP/full?target=10.1080/10407790.2019.1665386

In this paper, the inverse Cauchy problems in heat conduction under 3D func-
tionally graded materials (FGMs) with heat source are solved by using a semi-
analytical boundary collocation solver. In the present semi-analytical solver, the

combined boundary particle method and regularization technique is employed to
deal with ill-pose inverse Cauchy problems. The domain mapping method and
variable transformation are introduced to derive the high-order general solutions
satisfying the heat conduction equation of 3D FGMs. Thanks to these derived
high-order general solutions, the proposed scheme can only require the boundary
discretization to recover the solutions of the heat conduction equations with a heat
source. The regularization technique is used to eliminate the effect of the noisy
measurement data on the accessible boundary surface of 3D FGMs. The efficiency
of the proposed solver for inverse Cauchy problems is verified under several typical
benchmark examples related to 3D FGM with specific spatial variations (quadratic,
exponential and trigonometric functions).