A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec elements. The shape functions are classified into several categories with respect to their ...A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec 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 orthogonaiity. 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 quasi- stiffness 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.展开更多
We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality.The basis functions are grouped into edge and interior functions,and the later is further group...We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality.The basis functions are grouped into edge and interior functions,and the later is further grouped into normal and bubble functions.In our construction,the trace of the edge shape functions are orthonormal on the associated edge.The interior normal functions,which are perpendicular to an edge,and the bubble functions are both orthonormal among themselves over the reference element.The construction is made possible with classic orthogonal polynomials,viz.,Legendre and Jacobi polynomials.For both the mass matrix and the quasi-stiffness matrix,better conditioning of the new basis is shown by a comparison with the basis previously proposed by Ainsworth and Coyle[Comput.Methods.Appl.Mech.Engrg.,190(2001),6709-6733].展开更多
文摘A partially orthonormal basis is constructed with better conditioning properties for tetrahedral H（curl）-conforming Nedelec 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 orthogonaiity. 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 quasi- stiffness 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.
基金The research was supported in part by a DOE grant 304(DEFG0205ER25678)a NSFC grant(10828101).
文摘We construct a well-conditioned hierarchical basis for triangular H(curl)-conforming elements with selected orthogonality.The basis functions are grouped into edge and interior functions,and the later is further grouped into normal and bubble functions.In our construction,the trace of the edge shape functions are orthonormal on the associated edge.The interior normal functions,which are perpendicular to an edge,and the bubble functions are both orthonormal among themselves over the reference element.The construction is made possible with classic orthogonal polynomials,viz.,Legendre and Jacobi polynomials.For both the mass matrix and the quasi-stiffness matrix,better conditioning of the new basis is shown by a comparison with the basis previously proposed by Ainsworth and Coyle[Comput.Methods.Appl.Mech.Engrg.,190(2001),6709-6733].
