Research On Finite Difference Algorithm For Efficient Lagr Alzheimer 's Time Domain

The finite-difference time-domain (FDTD) method has been widely used for manyelectromagnetic problems. The FDTD method based on weighted Laguerre polynomials(WLP-FDTD) untilizes Yee’s finite-difference scheme in the space-domain, and spanselectromagnetic fields in the time-domain in terms of the orthogonal basisfunctions-weighted Laguerre polynomials. The method is not restricted by theCourant-Friedrich-Levy stability condition. However, the WLP-FDTD method produced ahuge sparse matrix equation, which determines the CPU time and memory storage.Efficient algorithms for implementing the WLP-FDTD method are introduced. Numericalresults indicated that the efficient algorithms can save CPU time and memory storagegreatly while maintaining comparable computational accuracy. However, the splitting errorassociated with the perturbation term becomes pronounced in regions with larger spatialderivatives of the field. In this dissertation, the new efficient algorithms for implementingthe WLP-FDTD method are studied. The main contributions are as follows:1. We presented a new efficient2-D WLP-FDTD algorithm based on the use of aniterative procedure to reduce the splitting error. The new algorithm does not involve anynonphysical intermediate variables, and its update equations are much simpler and moreconcise than the original ones. Instead of applying the iterative procedure uniformly to theentire computational domain, one can apply an additional number of iterations to regionswith relatively large field variation. Using this approach, the overall accuracy can beimproved with little computational overhead.2. We extended the new2-D efficient algorithm to a full3-D wave. Numericalformulations of the new3-D Laguerre-based FDTD method were devised. For modelingsome regions with larger spatial derivatives of the field, the new algorithm shows betterperformance than the original one. We numerically verify that, at the comparableaccuracy， the efficiency of the proposed method with an iterative procedure is superior tothe FDTD method and theADI-FDTD method.3. We presented a theoretical analysis to verify the convergence of the proposediterative method, and the time-subsection technique was given for the the new efficientWLP-FDTD method. By using the numerical experiments about a PEC box, the stability ofthe iterative procedure for the new efficient3-D WLP-FDTD method had been proved.4. The anisotropic-medium PML, CPML and splitted-field PML absorbingboundary conditions for new2-D and3-D efficient WLP-FDTD methods were introduced,and its absorbing performance is studied as a function of the constitutive parameters of thePML.