Agent Navigation via Harmonic Potentials with Half-Sweep Kaudd Successive Over Relaxation (HSKSOR) Method

Musli, Farhah Athirah; Saudi, Azali

doi:10.1109/iscaie.2019.8744002

Cited by 2 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A variant of KSOR was applied to solve parabolic equations Muhiddin et al (2020), while faster Half-Sweep KSOR was employed in the previous works to reduce the amount of computation (Suardi et al, 2017;Musli and Saudi, 2019). The Kaudd Accelerated Over Relaxation (KAOR) was later introduced by Youssef and Farid (2015) for solving linear systems.…”

Section: Introductionmentioning

confidence: 99%

Agent Navigation based on Boundary Value Problem using Iterative Methods

Musli,

Saudi

2023

JSML

View full text Add to dashboard Cite

This paper presents the simulation of numerical solutions to the navigational problem of an agent traveling safely in its environment. The approach is based on the numeric solutions of the boundary value problem (BVP) that generate harmonic potential fields through a differential equation whose gradient represents navigation routes to the destination. Two methods, namely KSOR and KAOR, were tested to solve the BVP. KSOR and KAOR are variants of the standard SOR and AOR methods, respectively. In this work, the KSOR and KAOR methods were used to solve the BVP by applying Laplace's equation to obtain harmonic functions. The generated harmonic functions are then utilized by the searching algorithm to find a smooth navigational route for an agent to travel in its environment without colliding with any obstacles. The numerical results from the solutions of BVP demonstrate that the KAOR provides a faster execution time with fewer iterations compared to the KSOR method.

show abstract

Section: Introductionmentioning

confidence: 99%

Agent Navigation based on Boundary Value Problem using Iterative Methods

Musli,

Saudi

2023

JSML

View full text Add to dashboard Cite

show abstract

“…In recent studies, the SOR and its variants were applied to solve problems in image processing [10] and agent navigation [11]. An extension to the SOR known as the Accelerated Overrelaxation (AOR) method that employs two acceleration parameters was later introduced by Hadjidimos [12].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Red–Black Skewed Modified Accelerated Arithmetic Mean Iterative Method for Solving Two-Dimensional Poisson Equation

Saudi

Dahalan

2022

Symmetry

Self Cite

View full text Add to dashboard Cite

This paper presents the extended variants to the established two-stage Arithmetic Mean (AM) method known as the Modified Accelerated Arithmetic Mean (MAAM) and Skewed Modified Accelerated Arithmetic Mean (SkMAAM) methods to solve the two-dimensional elliptic problem. The existing two-stage AM and its skewed variants apply one weighted parameter for the computation of nodes in Levels 1 and 2. The suggested MAAM and SkMAAM methods employ red–black ordering with two different weighted parameters and an additional two distinct accelerated parameters for red and black nodes, respectively. By carefully choosing optimum parameter values, the proposed MAAM and SkMAAM improve the computational execution of the algorithm. With red–black ordering, the computational molecules of red and black nodes are symmetrical, in which the computation of red nodes applies the updated values of their four neighbouring black nodes and vice versa. These symmetrical computational molecules of red and black nodes can be seen for the modified variants MAM and MAAM, and their corresponding skewed variants SkMAM and SkMAAM. The proposed MAAM and SkMAAM methods are compared to the existing AM and Modified AM (MAM) and their corresponding skewed variants, namely the Skewed AM (SkAM) and Skewed MAM (SkMAM) methods. The performance of the newly proposed MAAM and SkMAAM methods is compared against the existing methods in terms of computational complexity and actual execution time. It is shown in the simulation results that the skewed variants are superior to their corresponding regular variants, in which the SkMAAM method gives the best performance.

show abstract

Agent Navigation via Harmonic Potentials with Half-Sweep Kaudd Successive Over Relaxation (HSKSOR) Method

Cited by 2 publications

References 20 publications

Agent Navigation based on Boundary Value Problem using Iterative Methods

Agent Navigation based on Boundary Value Problem using Iterative Methods

An Efficient Red–Black Skewed Modified Accelerated Arithmetic Mean Iterative Method for Solving Two-Dimensional Poisson Equation

Contact Info

Product

Resources

About