For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It defines the local projectors and the local degrees of freedom with respect to a set of scaled monomials recomputed on more well-shaped polytopes. This new approach is less computationally demanding than using the orthonormal polynomial basis. The effectiveness of our procedure is tested on different numerical examples characterized by challenging geometries of increasing complexity.
翻译:在 2D 和 3D 虚拟元素方法 (VEM) 中, 提出了一种新方法, 用于在存在不良形状多面体的情况下提高局部和全局矩阵的条件数。该方法使用一组在更加规则的多面体上重新计算得到的标度单项式来定义局部投影矩阵和局部自由度。相比使用正交多项式基础的方法, 这种新方法的计算速度更快。通过对不同复杂度的具有挑战性的几何形状进行测试, 证明了本方法的有效性。