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

Keberkesanan kaedah pengenduran berlebihan teritlak terhadap penyelesaian masalah nilai sempadan dua dimensi

Masalah nilai sempadan sering ditemui dalam transmisi gelombang. Kertas ini membincang tiga kaedah berangka berjenis pengenduran berlebihan bagi menyelesai masalah nilai sempadan. Kaedah yang dibincang ialah Pengenduran Berlebihan Berturut-turut (PBB),Pengenduran Berlebihan Terpecut (PBT) dan Pengenduran Berlebihan Berturut-turut Terputar (PBBT). Dalam kertas ini, formulasi umum (teritlak) dibangun bagi ketiga-tiga kaedah ini. Hasil kajian menunjukkan kaedah PBT Teritlak dan PBB Teritlak menghasil kejituan tertinggi, manakala kaedah PBBT Teritlak merupakan kaedah penyelesaian terpantas

A new Quarter-Sweep Arithmetic Mean (QSAM) method to solve diffusion equations

The aim of this paper is to introduce the Quarter-Sweep Arithmetic Mean (QSAM) method using the Quarter-Sweep Crank-Nicolson (QSCN) finite difference method for solving one-dimensional diffusion equations. The formulation of the QSAM method is developed by combining the concept of the quartersweep iteration and the Arithmetic Mean (AM) method known as one of two-step iterative methods. The QSAM method has been shown to be very fast as compared to the standard AM method. Some numerical tests were included to support our statement

A Method of Computing Functions of Trapezoidal Fuzzy Variable and Its Application to Fuzzy Calculus

This paper introduces a method of computing functions of trapezoidal fuzzy variable. The method is based on the implementation of an unconstrained optimisation technique over the α -cut of fuzzy interval. To show the effectiveness of the proposed method, we provide several numerical examples in computing the solutions of linear and non-linear fuzzy differential equations. The final results showed that the proposed method is capable to generate convex fuzzy solutions on time domain

Half-sweep algebraic multigrid (HSAMG) method applied to diffusion equations

In previous studies, the efficiency of the Half-Sweep Multigrid (HSMG) method has been shown to be very fast as compared with the standard multigrid method. This is due to its ability to reduce computational complexity of the standard method. In this paper, the primary goal is to propose the Half-Sweep Algebraic Multigrid (HSAMG) method using the HSCN finite difference scheme for solving two-dimensional diffusion equations. The formulation of the HSAMG scheme is derived by borrowing the concept of the HSMG method. Results on some numerical experiments conducted show that the HSAMG method is superior to the standard algebraic method

Quarter-sweep iterative alternating decomposition explicit algorithm applied to diffusion equations

The aim of this article is to describe the formulation of the quarter-sweep iterative alternating decomposition explicit (QSIADE) method using the finite difference approach for solving one-dimensional diffusion equations. The concept of the QSIADE method is inspired via combination between the quarter-sweep iterative and the iterative alternating decomposition explicit (IADE) methods known as one of the technique in two-step iterative methods. The QSIADE method has been shown to be very fast as compared with the standard IADE method. Some numerical tests were included to support our statement

Complexity reduction approach for solving hyperbolic problems

Complexity reduction approach has been used to solve various science and technology problems. In this paper we will discuss the implementation of the approach to solve some hyperbolic equation such as first order hyperbolic problem and the Maxwell Equations. For solving the Maxwell equations, we implement a weighted average fourth order truncation with the complexity reduction approach. The approach shown to successfully reduce the complexity of original method. Results show to increase the speed up of its original method significantly

Scilab solution to genetic network problem

Genetic networks can be represented by a system of ordinary differential equations. These representations give the opportunity for researchers to simulate the behaviour of its gene numerically. In this paper, we apply two fourth order methods, namely Adam-Bashforth-Moultan (an implicit method which produce a very high accuracy solution) and fourth order Runge-Kutta (an explicit method which also produce a very high accuracy solution) using a free open source software named Scilab. We use both methods to simulate problem in toggle switch and biological clock of Neurospora Crassa. Finding shows that both methods perform well in simulating toggle switch and biological clock problem. Simplistic approach but outstanding solution (output) gathered via Scilab was the main attractive characteristic for using the software. Choosing Scilab was very relevant and beneficial for solving problem numerically. Usage of the software will reduce organization budget in teaching and learnin

Heat simulation via scilab programming

This paper discussed the used of an open source sofware called Scilab to develop a heat simulator. In this paper, heat equation was used to simulate heat behavior in an object. The simulator was developed using finite difference method. Numerical experiment output show that Scilab can produce a good heat behavior simulation with marvellous visual output with only developing simple computer code