The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing theMaxwell’s equations.It is based on splitting the whole Maxwell’s equations and matching the x-d...The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing theMaxwell’s equations.It is based on splitting the whole Maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically.In this paper,we make further study on the scheme for the 2D Maxwell’s equations with the PEC boundary condition.Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H^(1)-norm are derived.It is then proved that the scheme is unconditionally stable in the discrete H^(1)-norm.By the new energy-conserved identities,the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H^(1)-norm.Numerical experiments are carried out and confirm our theoretical results.展开更多
We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of （D（h） order...We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of （D（h） order in energy norm and of O（h2） order in L2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O（h2） order in energy norm, and the convergence rate in L2 norm is still of O（h2） order, which cannot be improved. Numerical examples are presented to demonstrate our theoretical results.展开更多
The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived wit...The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived with their remainder expressions.展开更多
基金The work of L.Gao was supported by Shandong Provincial Natural Science Foundation(Y2008A19)Shandong Provincial Research Reward for Excellent Young Scientists(2007BS01020)and the Scientific Research Foundation for the Returned Chinese Scholars,State Education Ministry.The work of D.Liang was supported by Natural Sciences and Engineering Research Council of Canada.We are very grateful to the anonymous referees for their valuable suggestions which have helped to improve the paper.
文摘The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing theMaxwell’s equations.It is based on splitting the whole Maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically.In this paper,we make further study on the scheme for the 2D Maxwell’s equations with the PEC boundary condition.Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H^(1)-norm are derived.It is then proved that the scheme is unconditionally stable in the discrete H^(1)-norm.By the new energy-conserved identities,the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H^(1)-norm.Numerical experiments are carried out and confirm our theoretical results.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471026, 11271035, 91430213, 11421101 and 11101415)
文摘We present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of （D（h） order in energy norm and of O（h2） order in L2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O（h2） order in energy norm, and the convergence rate in L2 norm is still of O（h2） order, which cannot be improved. Numerical examples are presented to demonstrate our theoretical results.
基金supported by the National Natural Science Foundation of China(Grant No.10471128).
文摘The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived with their remainder expressions.
