Computational Engineering Advancements: General Review of Mathematical Modeling in Computer Engineering Applications

Abstract

The comprehensive review explored the advancements in computational engineering with a focus on the role of mathematical modeling in computer engineering applications. The research investigated various mathematical models that used in different computer engineering fields, including software engineering, hardware design, and networking. It also examined the importance of mathematical modeling and its impact on solving complex engineering problems. The study highlighted emerging trends in mathematical modeling, such as reduced-order modeling, multiscale modeling, and uncertainty quantification. It also explored cutting-edge computational tools and techniques, such as high-performance computing, GPU acceleration, and meshless methods, which enabled engineers to conduct more efficient and accurate simulations. Furthermore, the integration of artificial intelligence and machine learning in mathematical modeling was discussed, emphasized the growing significance of data-driven models and surrogate modeling in computer engineering applications. The research identified industries that was benefit from enhanced computational engineering approaches, including aerospace, energy, healthcare, finance, and manufacturing. Through case studies, successful implementations of mathematical models in real-world engineering projects were presented, showcasing the practical implications of these advancements. The review also addressed challenges in adopting advanced mathematical models, such as computational complexity, data limitations, and model interpretability, and proposes potential solutions to address these issues.