In this paper, we shall give a group of new isoparametric elements suitable .for St.Wnant's torsion of a bar with vertical cracks. These elements are eight-pointisoparametric element, quarter eight-Point isoparame...In this paper, we shall give a group of new isoparametric elements suitable .for St.Wnant's torsion of a bar with vertical cracks. These elements are eight-pointisoparametric element, quarter eight-Point isoparametric element and eight-pointisoparametric transition element. Among these elements, the second and the thirdelements possess the singularity of order r-1/2 at crack tip. Using these elements, wehave completed the calculations of St. Venant's torsion for a cylinder with a radialvertical crack. The calculated results show that the isoparametric elements given bythis paper have ideal accuracy. good convergence. high speed of convergence, lowfreedom and little computational time, and so they can be widely applied to practice.展开更多
We analyze the convergence of multigrid methods applied to finite elementequations of second order with singularities caused by reentrant angles and abruptchanges in the boundary conditions. Provided much more weaker ...We analyze the convergence of multigrid methods applied to finite elementequations of second order with singularities caused by reentrant angles and abruptchanges in the boundary conditions. Provided much more weaker demand of clas-sical multigrid proofs, it is shown in this paper that, for symmetric and positivedefinite problems in the presence of singularities, multigrid algorithms with evenone smoothing step converge at a rate which is independent of the number of lev-els or unknowns. Furthermore, we extend this result to the nonsymmetric andindefinite problems.展开更多
文摘In this paper, we shall give a group of new isoparametric elements suitable .for St.Wnant's torsion of a bar with vertical cracks. These elements are eight-pointisoparametric element, quarter eight-Point isoparametric element and eight-pointisoparametric transition element. Among these elements, the second and the thirdelements possess the singularity of order r-1/2 at crack tip. Using these elements, wehave completed the calculations of St. Venant's torsion for a cylinder with a radialvertical crack. The calculated results show that the isoparametric elements given bythis paper have ideal accuracy. good convergence. high speed of convergence, lowfreedom and little computational time, and so they can be widely applied to practice.
文摘We analyze the convergence of multigrid methods applied to finite elementequations of second order with singularities caused by reentrant angles and abruptchanges in the boundary conditions. Provided much more weaker demand of clas-sical multigrid proofs, it is shown in this paper that, for symmetric and positivedefinite problems in the presence of singularities, multigrid algorithms with evenone smoothing step converge at a rate which is independent of the number of lev-els or unknowns. Furthermore, we extend this result to the nonsymmetric andindefinite problems.
