Performance comparison of TLM, FDTD and Haar wavelet MRTD algorithms for electromagnetic simulations

Abstract

The performance in computation time, computer memory and computation accuracy of the TLM, FDTD, 0-0rder and 1st-Order Haar wavelet MR.TD algorithms have been tested. The results show: (1) The FDTD algorithm is about 1.25 times as fast as TLM. The CPU runtimes for the 0- and 1st-Order MR.TD are almost the same as that of FDTD although much less time steps are required in the 0- and 1st-Order MRTD for the same time duration. The CPU runtimes linearly vary with the time step. Thus the CPU runtime of each algorithm is mainly determined by the number of variables that must be retrieved from, and stored in memory at each time step; (2) Because of the numerical comparison and memory reallocation in each time step, thresholding greatly increases computing load; (3) The 1st-Order Haar wavelet MRTD can save much more memory. The optimal relative threshold fraction is about 0.01 % and large memory savings are attainable while maintaining reasonable accuracy. But the CPU runtimes are too long for the 0-0rder and 1st-Order MRTD with thresholding technique. Thus the tradeoff between computational efficiency and memory saving should be taken into consideration. An optimum procedure and well-designed data structures are necessary to ensure that memory requirements are kept at a minimum while maintaining computational efficiency at the same time.