Solving Backward Heat Conduction Problems Using a Novel Space–Time Radial Polynomial Basis Function Collocation Method

Applied Sciences

Ming-Ren Chen¹  Cheng-Yu Ku²  Jing-En Xiao³  Chih-Yu Liu³ 

[1] Center for Occupational Safety and Health, National Taiwan Ocean University, Keelung City 20224, Taiwan;Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung City 20224, Taiwan;Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung City 20224, Taiwan;

关键词: collocation method;    space–time;    radial polynomial;    basis function;    heat conduction;   

DOI  :  10.3390/app10093215

来源: DOAJ

【 摘 要 】

In this article, a novel meshless method using space–time radial polynomial basis function (SRPBF) for solving backward heat conduction problems is proposed. The SRPBF is constructed by incorporating time-dependent exponential function into the radial polynomial basis function. Different from the conventional radial basis function (RBF) collocation method that applies the RBF at each center point coinciding with the inner point, an innovative source collocation scheme using the sources instead of the centers is first developed for the proposed method. The randomly unstructured source, boundary, and inner points are collocated in the space–time domain, where both boundary as well as initial data may be regarded as space–time boundary conditions. The backward heat conduction problem is converted into an inverse boundary value problem such that the conventional time–marching scheme is not required. Because the SRPBF is infinitely differentiable and the corresponding derivative is a nonsingular and smooth function, solutions can be approximated by applying the SRPBF without the shape parameter. Numerical examples including the direct and backward heat conduction problems are conducted. Results show that more accurate numerical solutions than those of the conventional methods are obtained. Additionally, it is found that the error does not propagate with time such that absent temperature on the inaccessible boundaries can be recovered with high accuracy.

【 授权许可】

Unknown