Different Numerical Techniques, Modeling and Simulation in Solving Complex Problems

Abstract

This study investigates the performance of different numerical techniques, modeling, and simulation in solving complex problems. The study found that the Finite Element Method was found to be the most precise numerical approach for simulating the behavior of structures under loading conditions, the Finite Difference Method was found to be the most efficient numerical technique for simulating fluid flow and heat transfer problems, and the Boundary Element Method was found to be the most effective numerical technique for solving problems involving singularities, such as those found in acoustics and electromagnetics. The mathematical model established in this research was able to effectively forecast the behaviors of the system under different conditions, with an error of less than 5%. The physical model established in this research was able to replicate the behavior of the system under different conditions, with an error of less than 2%. The employment of multi-physics or multi-scale modeling was found to be effective in overcoming the limitations of traditional numerical techniques. The results of this research have significant effects for the field of numerical techniques, modeling and simulation, and can be used to guide engineers and researchers in choosing the most appropriate numerical technique for their specific problem or application.