A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction

This study documents the first attempt to apply a nonsingular indirect boundary element method (BEM) for the solution of three-dimensional (3D) inverse heat conduction problems. The present BEM formulation avoids the calculation of hyper-singular integrals. Furthermore, the exact geometrical representation of computational domain is adopted by parametric equations to eliminate the errors in traditional approaches of polynomial shape functions. Due to its boundary-only discretizations and semi-analytical nature, the proposed method can be viewed as a competitive candidate for the solution of inverse problems. Four benchmark numerical examples indicate that the proposed method, in conjunction with proper regularization techniques, is accurate, computationally efficient and numerically stable for the solution of 3D inverse problems subjected to various levels of noise in input data.