A novel formulation for heat conduction using non-convex meshes based on smoothed finite element method

A novel formulation for non-convex polygon mesh based on cell-based smoothed finite element method (CSFEM) is presented for analyzing heat conduction. The major ingredient of this article include: 1) An inverse coordinate mapping method is proposed by using arbitrary polygons of shapes such as "dog", "bird", "cow" obtained from images to discretize the problem domain; 2) The Ear clipping triangulation technique is used to construct a triangular smoothing domain consisting only of field nodes; 3) The element integral is transformed into the boundary integral of triangular smoothing domain, thereby achieving temperature gradient smoothing operation, using the gradient smoothing technique, Well behaved smoothed stiffness matrix is achieved through the gradient smoothing technique of S-FEM in concave polygon elements without the need to construct additional stability terms. Based on the weakened weak form theory, the discretized system equations of heat conduction problem are established, which a symmetric and well-conditioned. The efficacy and robustness of the proposed method has been has been demonstrated through a number of benchmark examples including multi- material systems. It can effectively solve heat conduction problems using concave polygon elements, allowing materials with complex configuration being effectively modeled.