ENME E4363: Multiscale Computational Science and Engineering
Discover how to bridge the gap between atoms and structures in this cutting-edge course on Practical Multiscaling. Guided by Professor Fish and his authoritative textbook, you'll gain the tools to model complex engineering systems across multiple scales—from nanomaterials to aerospace components. Whether you're optimizing designs or exploring advanced materials, you'll master multiscale techniques that bring both precision and efficiency to real-world problem solving.
Course Overview
This course will equip you with both the theoretical foundations and practical skills necessary to tackle engineering problems involving multiple spatial and temporal scales—ranging from the atomistic level to macroscopic systems.
The course is built around Practical Multiscaling, a textbook authored by course instructor, Professor Fish, which emphasizes the formulation of multiscale methods and their application to real-world engineering systems. From aerospace structures and nanocomposites to emerging applications in energy and healthcare, you’ll apply multiscale approaches to understand and predict material behavior, optimize designs, and reduce development costs.
The curriculum covers key topics such as homogenization techniques, coarse-graining, hierarchical and concurrent multiscale methods, and the integration of fine-scale physics into macro-level simulations. Special attention is given to the trade-offs between accuracy and computational cost, and how to evaluate whether a multiscale approach is justified for a given problem. You will learn how to perform upscaling and downscaling, implement multiscale finite element methods, and handle nonlinear and history-dependent material behaviors that traditional models fail to capture.
You’ll also gain hands-on experience with computational tools that are widely used in research and industry. This includes custom multiscale simulation frameworks and commercially relevant software like the Multiscale Designer, developed from the instructor’s own research and now used by companies across aerospace, automotive, and electronics sectors. These tools not only help reinforce concepts taught in the classroom but will also prepare you to engage directly with industrial workflows and digital engineering platforms.
Ultimately, this course responds to a growing societal demand for engineers who can model, simulate, and innovate across multiple scales. These advanced skills are critical to designing modern engineered systems—from sustainable materials and advanced manufacturing to cutting-edge biomedical devices. The methods taught on this course are not just academically rigorous but are deployed in industries shaping the future, making this course both intellectually rich and professionally relevant.
Course Instructor
Jacob Fish
Robert A.W. and Christine S. Carleton Professor of Civil Engineering
Professor Jacob Fish is a leading authority in nonlinear computational mechanics with extensive contributions to the development of advanced numerical methods for nonlinear systems. His career spans over three decades of academic leadership, industrial collaboration, and groundbreaking research in nonlinear multiscale modeling, computational plasticity, damage mechanics, and coupled field problems. As the founding Director of Columbia's Multiscale Science and Engineering Center, his work has focused on creating robust and efficient algorithms capable of addressing the nonlinear behavior of materials and structures under complex loading conditions. His research has influenced simulation tools used in the aerospace, automotive, defense, and energy sectors.