Computational Mathematics and Numerical Simulation for Smart Engineering Systems and Sustainable Infrastructure https://doi.org/10.21276/AATCCReview.2025 Mateo Ricci https://orcid.org/register Yuki Nakamura https://orcid.org/register Amara Ndlovu https://orcid.org/register Claire Dubois https://orcid.org/register Omar Haddad https://orcid.org/register Viktor Petrov https://orcid.org/register Sofia Ribeiro https://orcid.org/register Ethan McAllister https://orcid.org/register Leila Farouk https://orcid.org/register Jonas Bergström https://orcid.org/register Computational mathematics and numerical simulation have become essential tools for solving complex engineering problems and supporting sustainable infrastructure development. These techniques enable engineers to model, analyze, and optimize systems before physical implementation, reducing cost, time, and material consumption. Numerical methods such as the Finite Element Method (FEM), Finite Difference Method (FDM), and Finite Volume Method (FVM) are widely used in structural analysis, fluid dynamics, heat transfer, and energy systems. Recent advancements in artificial intelligence (AI), digital twins, and high-performance computing have further improved simulation accuracy and decision-making. This review highlights the importance of computational mathematics, major numerical simulation methods, their applications in smart engineering systems, and their contribution to sustainable infrastructure. It also discusses current challenges and future research directions for developing efficient, reliable, and environmentally friendly engineering solutions.

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Short Communication
Mateo Ricci1 Yuki Nakamura2 Amara Ndlovu3 Claire Dubois4 Omar Haddad5 Viktor Petrov6 Sofia Ribeiro7 Ethan McAllister8 Leila Farouk9 Jonas Bergström10
1 Department of Computational Mathematics, European Institute for Mathematical Engineering, Milan, Italy
2 Department of Applied Mathematics and Computational Science, Pacific Centre for Advanced Engineering Research, Kyoto, Japan
3 School of Mathematical Sciences, Southern African Institute of Computational Engineering, Pretoria, South Africa
4 Department of Numerical Analysis and Scientific Computing, Centre for Sustainable Engineering Mathematics, Lyon, France
5 Department of Civil and Computational Engineering, Middle Eastern Institute for Smart Infrastructure, Amman, Jordan
6 Laboratory of Computational Mechanics and Numerical Modelling, Eastern European Institute of Engineering Sciences, Sofia, Bulgaria
7 Department of Applied Computational Science, Atlantic Institute for Sustainable Technology, Lisbon, Portugal
8 School of Engineering Mathematics, North American Centre for Smart Infrastructure Research, Vancouver, Canada
9 Department of Computational Modelling and Data Science, North African Institute of Engineering Innovation, Tunis, Tunisia
10 Department of Numerical Simulation and Sustainable Systems, Nordic Centre for Computational Engineering, Stockholm, Sweden
https://doi.org/10.21276/AATCCReview.2025

Abstract

Computational mathematics and numerical simulation have become essential tools for solving complex engineering problems and supporting sustainable infrastructure development. These techniques enable engineers to model, analyze, and optimize systems before physical implementation, reducing cost, time, and material consumption. Numerical methods such as the Finite Element Method (FEM), Finite Difference Method (FDM), and Finite Volume Method (FVM) are widely used in structural analysis, fluid dynamics, heat transfer, and energy systems. Recent advancements in artificial intelligence (AI), digital twins, and high-performance computing have further improved simulation accuracy and decision-making. This review highlights the importance of computational mathematics, major numerical simulation methods, their applications in smart engineering systems, and their contribution to sustainable infrastructure. It also discusses current challenges and future research directions for developing efficient, reliable, and environmentally friendly engineering solutions.

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