Inverse Heat Conduction Problem with a Nonlinear Source Term Through Radial Basis Function Partition of Unity Collocation Method

Jafarabadi, Ahmad

doi:10.311581/JAMDA.2509.1013.1.3.2

Inverse Heat Conduction Problem with a Nonlinear Source Term Through Radial Basis Function Partition of Unity Collocation Method

Document Type : Research Article

Author

Ahmad Jafarabadi

Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

10.311581/JAMDA.2509.1013.1.3.2

Abstract

This study focuses on determining the numerical solution for the surface heat flux history and temperature distribution in an inverse heat conduction problem (IHCP) with a nonlinear source term. The problem is addressed using a temperature over-specification condition as an energy over-specification condition across the computational domain. The proposed approach employs the radial basis function partition of unity collocation method combined with the finite difference method for temporal discretization. This meshless method eliminates the need for mesh generation, and its local formulation at each time step results in a sparse coefficient matrix, significantly reducing computational cost. Despite the problem having a unique solution, it remains ill-posed, as small perturbations in the input data can lead to large errors in the output. Numerical results demonstrate that the proposed method provides accurate solutions for exact data and maintains stability when handling noisy data.

Keywords

Partition of Unity (PU) method

Meshless interpolation

Inverse heat conduction problem

Surface heat flux