The Finite Element Method and Isogeometric Analysis: Past, Present, Future , Thomas Hugues

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; 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 (