The Finite Element Method, Computational Mechanics, and Isogeometric Analysis: Past, Present and Future

Thomas J.R. Hughes

Oden Institute for Computational Engineering and Sciences

Department of Aerospace Engineering and Engineering Mechanics

The University of Texas at Austin, 201 East 24th Street, Austin, Texas 78712, USA



I will begin by probing into the past to discover the origins of the Finite Element Method (FEM), and then trace the evolution of those early developments to the present day in which the FEM is ubiquitous in science, engineering, mathematics, and medicine, and the most important discretization technology in Computational Mechanics.


However, despite its enormous success, there are still problems with contemporary technology, for example, building meshes from Computer Aided Design (CAD) representations is labor intensive, and a significant bottleneck in the design-through-analysis process. Other deficiencies are the introduction of geometry errors in computational models that arise due to feature removal, geometry clean-up and CAD “healing,” necessary to facilitate mesh generation, the inability of contemporary technology to “close the loop” with design optimization, and the failure of higher-order finite elements to achieve their full promise in industrial applications. These issues are addressed by Isogeometric Analysis (IGA), the vision of which was first presented in a paper published October 1, 2005 [1]. Since those seminal ideas, the subject has progressed enormously and a number of advantages of IGA FEM over traditional FEM have become manifest.


I will very briefly present the motivation leading to IGA, its status, recent progress, areas of current activity, and what it offers for analysis model development and the design-through-analysis process.


Finally, I will speculate on the future of Computational Mechanics, the technologies that will prevail, computer developments, and the role of Machine Learning.





[1] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, “Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement,” Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.