Inverse determination of boundary conditions in steady heat conduction with heat generation
Conference
Martin, TJ, Dulikravich, GS. (1995). Inverse determination of boundary conditions in steady heat conduction with heat generation
. American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, 312(10),
Martin, TJ, Dulikravich, GS. (1995). Inverse determination of boundary conditions in steady heat conduction with heat generation
. American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, 312(10),
Our unique inverse methodology for finding unknown boundary conditions for Laplace equation utilizing the Boundary Element Method (BEM) has been extended to the solution of two-dimensional inverse (ill-posed) Poisson problem of steady heat conduction with heat sources and sinks. The procedure is simple, reliable, non-iterative and cost effective. Accurate results in two-dimensional heat conduction with arbitrary distributions of heat sources have been obtained for several test cases where boundary conditions were unknown on certain boundaries. Because of its non-iterative, direct nature, our algorithm does not amplify errors in the over-specified input data supplied to parts of the boundary. Furthermore, it does not require regularization schemes, extrapolation to the boundary or mollification to suppress the amplification of input errors. Instead, a straight-forward modification to the BEM produces a single, highly singular solution matrix which we solved using a singular value decomposition matrix solver. Our method for the solution of ill-posed boundary condition problems governed by the Poisson equation also accepts input data at isolated interior points.
