ON THE CONSTRUCTION OF WELL-CONDITIONED HIERARCHICAL BASES FOR TETRAHEDRAL H(curl)-CONFORMING N(E)D(E)LEC ELEMENT

• 来源期刊: 计算数学（英文版）
• 关键词: Hierarchical bases Tetrahedral H(curl)-conforming elements Matrix conditioning
• 年，卷（期）: 2011,（5）
• 页码范围: 526-542
• 页数: 17页
• 语种: 英文
• DOI: 10.4208/jcm.1103-m3464

摘要

A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H(curl)-conforming Nédélec elements.The shape functions are classified into several categories with respect to their topological entities on the reference 3-simplex.The basis functions in each category are constructed to achieve maximum orthogonality.The numerical study on the matrix conditioning shows that for the mass and quasi-stiffness matrices,and in a logarithmic scale the condition number grows linearly vs. order of approximation up to order three.For each order of approximation,the condition number of the quasi-stiffness matrix is about one order less than the corresponding one for the mass matrix.Also,up to order six of approximation the conditioning of the mass and quasistiffness matrices with the proposed basis is better than the corresponding one with the Ainsworth-Coyle basis Internat.J.Numer.Methods.Engrg.,58:2103-2130,2003.except for order four with the quasi-stiffness matrix.Moreover,with the new basis the composite matrix μM + S has better conditioning than the Ainsworth-Coyle basis for a wide range of the parameter μ.