摘要：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.
