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：针对二维与三维虚拟单元法（Virtual Element Method, VEM），本文提出了一种新方法，以改善存在畸形多面体时局部与全局矩阵的条件数。该方法基于在形状更规整的多面体上重新计算的一组缩放单项式，定义了局部投影算子与局部自由度。相较于使用正交多项式基，该新方法的计算代价更低。通过不同数值算例验证了所提方法的有效性，这些算例具有复杂度递增的挑战性几何特征。