Hexahedral mesh quality improvement via edge-angle optimization

Abstract

We introduce a simple and practical technique to untangle and improve hexahedral (hex-) meshes. We achieve that by enabling the deformation of the boundary surfaces during the untangling process, which provides more space to reach a valid solution. To improve the element quality, an angle-based optimization strategy is proposed, which has much simpler formulation than the existing methods. The deformed volume after optimization is then pulled back to the original one using an inversion-free deformation. In contrast to the current methods, we perform the untangling and quality improvement within a few local regions surrounding elements with undesired quality, which can effectively improve the minimum scaled Jacobian (MSJ) quality of the mesh over the state-of-the-art method. We demonstrate the effectiveness of our methods by applying it to hex-meshes generated by a range of methods.