Fast Finite Difference Time Domain Algorithms for Solving Antenna Application Problem

This thesis describes the implementations of new parallel and sequential algorithms for electromagnetic wave propagation from a monopole antenna. Existing method, known as FDTD needs a very long processing time to solve this problem. The objective of the thesis is to develop new sequential and parallel algorithms that are faster than the standard Finite Difference Time Domain method. In this thesis, a SMP machine, the Sun Fire V1280 using six existing processors is used to solve 1D and 2D free space Maxwell equations with perfectly conducting boundary and absorbing boundary conditions. Complexity reduction approach concept is used to develop these algorithms. This approach split the solution domain into 1 3 and 2 3 compartments in 1D case and 1 9 and 8 9 compartments in 2D cases. Only 1 3 and 1 9 parts of the solution domain are solved in the main looping construct for problem in 1D and 2D, while the remaining points are solved outside the loop. The solutions to both parts are discussed in details in this thesis. These new parallel and sequential finite difference time domain (FDTD) algorithms yield from O(h2), ordinary O(h4) and weighted average O(h4) centered difference discretization using direct-domain and temporary-domain are used to solve problems mentioned above. In parallel implementation, techniques such as static scheduling, data decomposition and load balancing is used. Based on experimental results and complexity analysis, these new sequential and parallel algorithms are compared with the standard sequential and parallel FDTD algorithms, respectively. Results show that these new sequential and parallel algorithms run faster than the standard sequential and parallel FDTD algorithms. Beside that, formulation of a new higher accuracy second order method, which is called improved high speed low order finite difference time domain (IHSLO-FDTD) with direct-domain and temporary-domain are also proposed to solve the same problem are also described. Results show that, the IHSLO-FDTD with direct-domain and temporary-domain approaches are more efficient and economical. In general, almost all new proposed methods are more economical and run faster (except the Weighted Average High Speed High Order Finite Difference Time Domain (WAHSHO-FDTD) in directdomain and temporary-domain for 1D case) compared to the standard FDTD method for 1D and 2D case especially for IHSLO-FDTD.

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