3D anisotropic transient heat conduction by the local point interpolation-boundary element method. (30th October 2021) - Pierson, Gaël; Njiwa, Richard Kouitat
The boundary element method (BEM) is an effective numerical method for the solution of a large class of problems including heat conduction in isotropic media. The main appealing of this pure-BEM (reduction of the problem dimension by one) is tarnished to some extend when a fundamental solution to the governing differential equations does not exist. This is usually the case for anisotropic and nonlinear problems. Another attractive numerical approach due to its ease of implementation is the local point interpolation method applied to the strong form differential equations. The accuracy of this meshless method deteriorates in the presence of Neumann type boundary conditions. The main appealing of the BEM can be maintained by a judicious coupling of the pure-BEM with the local point interpolation method. The resulting approach, named the LPI-BEM, is shown to be effective for the solution of transient isotopic and anisotropic heat conduction.