The model of energy cost in a wireless sensor network （WSN）environment is built, and the energy awareness and the wireless interference mainly due to different path loss models are studied. A special case of a clust...The model of energy cost in a wireless sensor network （WSN）environment is built, and the energy awareness and the wireless interference mainly due to different path loss models are studied. A special case of a clustering scheme, a twodimensional grid clustering mechanism, is adopted. Clusterheads are rotated evenly among all sensor nodes in an efficient and decentralized manner, based on the residual energy in the battery and the random backoff time. In addition to transmitting and receiving packets within the sensors＇ electrical and amplification circuits, extra energy is needed in the retransmission of packets due to packet collisions caused by severe interference. By analysis and mathematical derivation, which are based on planar geometry, it is shown that the total energy consumed in the network is directly related to the gridstructure in the proposed grid based clustering mechanism. The transmission range is determined by cluster size, and the path loss exponent is determined by nodal separation. The summation of overall interference is caused by all the sensors that are transmitting concurrently. By analysis and simulation, an optimal grid structure with the corresponding grid size is presented, which balances between maximizing energy conservation and minimizing overall interference in wireless sensor networks.展开更多
This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving...This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.展开更多
This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test f...This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.展开更多
文摘The model of energy cost in a wireless sensor network （WSN）environment is built, and the energy awareness and the wireless interference mainly due to different path loss models are studied. A special case of a clustering scheme, a twodimensional grid clustering mechanism, is adopted. Clusterheads are rotated evenly among all sensor nodes in an efficient and decentralized manner, based on the residual energy in the battery and the random backoff time. In addition to transmitting and receiving packets within the sensors＇ electrical and amplification circuits, extra energy is needed in the retransmission of packets due to packet collisions caused by severe interference. By analysis and mathematical derivation, which are based on planar geometry, it is shown that the total energy consumed in the network is directly related to the gridstructure in the proposed grid based clustering mechanism. The transmission range is determined by cluster size, and the path loss exponent is determined by nodal separation. The summation of overall interference is caused by all the sensors that are transmitting concurrently. By analysis and simulation, an optimal grid structure with the corresponding grid size is presented, which balances between maximizing energy conservation and minimizing overall interference in wireless sensor networks.
基金supported by Natural Science Foundation of Shandong Province (GrantNo. Y2008A19)Research Reward for Excellent Young Scientists from Shandong Province (Grant No. 2007BS01020)National Natural Science Foundation of China (Grant No. 11071244)
文摘This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain （ADI-FDTD） method which is a popular scheme for solving the 3D Maxwell＇s equations. Precisely, for the case with a perfectly electric conducting （PEC） boundary condition we establish the optimal second-order error estimates in both space and time in the discrete Hi-norm for the ADI-FDTD scheme, and prove the approximate divergence preserving property that if the divergence of the initial electric and magnetic fields are zero, then the discrete L2-norm of the discrete divergence of the ADI-FDTD solution is approximately zero with the second-order accuracy in both space and time. The key ingredient is two new discrete modified energy norms which are second-order in time perturbations of two new energy conservation laws for the Maxwell＇s equations introduced in this paper. ~rthermore, we prove that, in addition to two known discrete modified energy identities which are second-order in time perturbations of two known energy conservation laws, the ADI-FDTD scheme also satisfies two new discrete modified energy identities which are second-order in time perturbations of the two new energy conservation laws. This means that the ADI-FDTD scheme is unconditionally stable under the four discrete modified energy norms. Experimental results which confirm the theoretical results are presented.
基金This research is supported by the ＇985＇ programme of Jilin University, the National Natural Science Foundation of China under Grant Nos. 10971082 and 11076014.
文摘This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.
