Generalized Higher Order Algorithms Based On Finite Difference Time Domain Method

Since 1966 the Finite Difference Time Domain method (FDTD) is introduced, it is used to research all kinds of electromagnetic problem by its good stability and applicability. In the recent years, the research of the electromagnetic scattering has become an important field of the computational electromagnetic. How to use the FDTD method to analyze the electromagnetic scattering also became a pop problem.Although the traditional FDTD has the good applicability, the computing accuracy is affected by the limit of numerical dispersion condition to the space grid size. The computation accuracy of the FDTD method used in the research of the complex target's electromagnetic scattering problem is low. To improve the accuracy of the traditional FDTD method, many new methods are introduced in the recent years to modify the traditional FDTD method which uses the centered difference with 2th order accuracy. In this paper the space difference uses the discrete singular convolution and the time difference uses the symplectic integrator propagator to improve the accuracy. The computational accuracy arise 4th order. A new general high order FDTD method is gotten. The research works with the new method are listed as follow。First in the 2D condition computing the transmit problem to compare the high order method with the traditional algorithm. To modify the space difference with the discrete singular convolution, the difference bandwidth reaches 2M order. The time difference uses the symplectic integrator propagator to enhance the time difference accuracy to 4th order. The computational result proves the high order algorithm has the same computational accuracy as the traditional algorithm.Then the modified high order FDTD algorithm is used to research the electromagnetic scattering problem. The connecting boundary and the PML absorbing boundary condition based on the symplectic integrator propagator and the discrete singular convolution are derived. The RCS of conducting cylinder are compared, which agrees well with the result of the published.To compute the 2D scattering character of multi-number conductivity cylinder is computed with big step-length to validate the applicability. The computational result shows the accuracy of the high order algorithm has better stability and computational efficiency, which has the same computational accuracy with the traditional algorithm. The modified algorithm could be used to compute the scattering problem of the big size and complex structure target.Based on the 2D result the near field scattering of the 3D square cylinder is computing. The near field distributing is gotten. The next work is to computing the far field value by the near to far transform.