Azali Saudi | Universiti Malaysia Sabah (original) (raw)

Papers by Azali Saudi

Harmonic functions are solutions to Laplace's equation that are known to have an ad... more Harmonic functions are solutions to Laplace's equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace's equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated pat...

Advanced Science Letters, 2017

Indonesian Journal of Electrical Engineering and Computer Science, 2021

In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional ... more In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization schemeto get the second-order SFD approximation equation. We propose a four-point similarity explicit group (4-point SEG) iterative methodasa numericalsolution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To showthe 4-point SEG iteration efficiency, two iterative methods, such as Jacobiand Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's perfo...

2018 IEEE International Conference on Artificial Intelligence in Engineering and Technology (IICAIET), 2018

Solving Poisson equation for seamless image blending is one of the powerful image editing tools. ... more Solving Poisson equation for seamless image blending is one of the powerful image editing tools. Thus, the aim of this paper is to evaluate the capability of the Quarter-Sweep Successive Over Relaxation (QSSOR) iterative methods in solving this problem. The finite difference discretization scheme is used to formulate the Poisson approximation equation. The concept and implementation of the proposed methods are presented. Finally, the numerical experimentations showed that QSSOR method has the best performance in blending time and number of iterations while generating the same quality of images compared to the Full-Sweep SOR (FSSOR) and Half-Sweep SOR (HSSOR).

Digital image composition deals with the problem of embedding portion of source image to the targ... more Digital image composition deals with the problem of embedding portion of source image to the target image to generate a single desirable image seamlessly. The aim is to produce a new image that combine both source and target images so that the seam between the two images is less noticeable. Image composition based on numerical differentiation using Laplacian operator to obtain the solution of Poisson equation is presented. The proposed method employs red-black strategy to speed up the computation by using an accelerated parameter to the existing relaxation method. This modified variant of relaxation method known as Modified Accelerated Over-Relaxation (MAOR) method is derived from the existing Modified Successive Over-Relaxation (MSOR) method. Several examples were tested to examine the effectiveness of the proposed method. The results showed that both modified accelerated variants performed faster than their corresponding standard modified successive variants.

The aim of this paper deals with the application of Half-Sweep Accelerated Over- Relaxation (HSAO... more The aim of this paper deals with the application of Half-Sweep Accelerated Over- Relaxation (HSAOR) iterative method using an unconditionally implicit finite difference approximation equation from the discretization of the onedimensional linear time-fractional diffusion equations by using the Caputo’s time fractional derivative. The Caputo’s implicit finite difference approximation equation leads a linear system which is solved by using the proposed HSAOR iterative method. Throughout implementations of two numerical experiments conducted, it has shown that the HSAOR method is superior as compared with FSAOR and FSOR methods.

Navigation problems of an agent in a virtual environment had been widely studied by many research... more Navigation problems of an agent in a virtual environment had been widely studied by many researchers. This paper presents a combination method based on Half-Sweep (HS) iteration and Kaudd Successive Over Relaxation (KSOR) to solve agent navigation problem in a simulated virtual environment. The proposed method, namely Half-Sweep Kaudd Successive Over Relaxation (HSKSOR), is used to obtain the solutions of Laplace’s equation known as harmonic functions which then be applied in the search algorithm to generate collision-free path for an agent to navigate from a specified start point to a target point. The results found that the HSKSOR offers faster computational approach with less computational time compared to the existing iterative methods.

Mobile robots are always in a state where they have to find a collision-free path in their enviro... more Mobile robots are always in a state where they have to find a collision-free path in their environment from start to the target point. This study tries to solve the problem of mobile robot iteratively by using a numerical technique. It is based on potential field technique that was modelled using the Laplace’s equation to restrain the creation of a potential functions across regions in the mobile robot’s configuration space. The gradient formed by the potential field is then used to generate a path for the robot to advance through. The present paper proposes a Two-Parameter Over-Relaxation (TOR) iterative method that is used to solve Laplace’s equation for obtaining the potential field that is then utilized for finding path of the robot, thus solving the robot pathfinding problem. The experiment indicates that it is capable of producing a smooth path between the starting and target points through the use of a finite-difference technique. Furthermore, the simulation results show that...

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2020 (MATHTECH 2020): Sustainable Development of Mathematics & Mathematics in Sustainability Revolution, 2021

Advanced Science Letters, 2018

In this paper, we deal with the application of Half-Sweep Accelerated Over Relaxation (HSAOR) met... more In this paper, we deal with the application of Half-Sweep Accelerated Over Relaxation (HSAOR) method with nonlocal discretization scheme for solving two-dimensional nonlinear elliptic boundary value problems. To do this, we propose a new nonlocal arithmetic mean scheme namely the four-point rotated nonlocal arithmetic mean scheme being imposed into any nonlinear term in the proposed problems. By using the second order finite difference scheme, the half-sweep nonlinear approximation equation has been derived. Then, the nonlocal discretization scheme is applied to transform the system of nonlinear approximation equations into the corresponding system of linear equations. Throughout numerical results, it can be pointed out that the proposed HSAOR method was superior in terms of number of iterations, execution time and maximum error compared to Full-Sweep Successive Over-relaxation (FSSOR) and Half-Sweep Successive Over Relaxation (HSSOR).

Journal of Physics: Conference Series, 2019

One of the main issues when dealing with mobile robot navigation is that we have to resolve the o... more One of the main issues when dealing with mobile robot navigation is that we have to resolve the obstacle avoidance problem, where when moving from a starting point to the goal point, the mobile robot will have to generate a collision-free path in order ensure that it can move efficiently in the environment. In this study, we attempt to resolve the issue by solving it iteratively via numerical technique. This solution is based on the potential field method that utilizes the Laplace’s equation to constrain the generation of potential functions over the regions in the configuration space where the mobile robot operates in. This paper proposed Modified Accelerated Over-Relaxation (MAOR) iterative method for solving robot path planning problem. Through the application of finite-difference technique in it, the experiment shows that the mobile robot is able to generate a smooth path from starting point to goal point. Furthermore, the results obtained from the simulation has shown that this...

Journal of Engineering and Applied Sciences, 2019

Journal of Computer Science & Computational Mathematics, 2019

Journal of Computer Science & Computational Mathematics, 2018

Malaysian Journal of Science, 2019

Jurnal Teknologi, 2016

This paper presents our study on a simulation of path planning for indoor robot that relies on th... more This paper presents our study on a simulation of path planning for indoor robot that relies on the use of Laplace’s equation to constrain the generation of Harmonic Potential Fields (HPF). The computation of HPF requires immense amount of computing resources, particularly when the size of environment is large. In the past, fast iterative methods that apply the use of half-sweep iteration and block technique are suggested. In this study, faster iterative method known as Four Point-Explicit Decoupled Group Successive Over relaxation via 9-Point Laplacian (4-EDGSOR-9L) is introduced. Essentially, the 4-EDGSOR-9L is actually a variant of block SOR iterative method based on four points that employs half-sweep iteration and utilizes 9-Point Laplacian discretization scheme. Once the HPF is obtained, the standard Gradient Descent Search (GDS) technique is performed for path tracing to the goal point.

2013 The International Conference on Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE), 2013

$Research paper thumbnail of Solving the time fractional diffusion equations by the Half-Sweep SOR iterative method$

2014 International Conference of Advanced Informatics: Concept, Theory and Application (ICAICTA), 2014