Abstract
In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted to solve the inverse heat conduction problem by approximating numerical solutions using Trefftz base functions satisfying the governing equation. The validity of the proposed method is established for a number of test problems. We compared the accuracy of the proposed method with that of the Trefftz method based on exponential basis functions. Results demonstrate that the proposed method obtains highly accurate numerical solutions and that the boundary data on the inaccessible boundary can be recovered even if the accessible data are specified at only one-fourth of the overall spacetime boundary.
Highlights
The inverse heat conduction problem (IHCP) is a crucial issue in various physical, precision mechanical, and industrial mechatronic applications.[1,2,3] Among IHCPs, the absence of the initial temperature of the heat conduction problem is referred to as a final boundary value problem or the backward heat conduction problem (BHCP)
The initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary
A novel spacetime collocation meshless method for solving the IHCP has been developed. This pioneering study is based on the spacetime collocation Trefftz method (SCTM) and provides a promising solution for the IHCP
Summary
The inverse heat conduction problem (IHCP) is a crucial issue in various physical, precision mechanical, and industrial mechatronic applications.[1,2,3] Among IHCPs, the absence of the initial temperature of the heat conduction problem is referred to as a final boundary value problem or the backward heat conduction problem (BHCP). The number of boundary collocation points in time domain is considered to be 90, which uniformly placed on both left and right sides of the spacetime boundary.
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