High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

In this work, by extending the method of Hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

In this paper,two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed as a generalized model from the nonlinear beam equation.Differing from the existing compact finite difference schemes which preserve the total energy in a recursive sense,the new schemes are proved to per-fectly preserve the total energy in the discrete sense.By using the standard energy method and the cut-off function technique,the optimal error estimates of the numerical solutions are established,and the convergence rates are of O(h^(4)+τ^(2))with mesh-size h and time-step τ.In order to improve the computational efficiency,an iterative algorithm is proposed as the outer solver and the double sweep method for pentadiagonal linear algebraic equations is introduced as the inner solver to solve the nonlinear difference schemes at each time step.The convergence of the iterative algorithm is also rigorously analyzed.Several numerical results are carried out to test the error estimates and conservative properties.

Tensor-Based Joint Channel Estimation and Symbol Det ection for AF MIMO Relay Networks

A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward(AF)relaying approach.The encoding scheme at the source node introduces the time-domain spreading with a time-varying linear constellation precoding.Then,a set of amplifying factors matrices is utilized by the relays to amplify and forward the received data to the destination.The received signal at the destination can be construe ted as a fourth-order tensor model,which is referred to as the nested parallel factor(PARAFAC)model.And then,we present a novel Levenberg-Marquardt(LM)algorithm based on this tensor model.The proposed method does not require complex signal processing at the relay,which effectively reduces the burden of relay.As a semi-blind method,which does not require the pilot signal,the proposed receiver can jointly recover the channels and information symbols.Moreover,the proposed semi-blind receiver is robust as it can work in different wireless channel scenarios.Simulations are conducted to demonstrate the efficiency of the proposed semi-blind approach.