Conservation of Geometry in Numerical Simulation: A Primer on Isogeometric Analysis
Date and time:
Friday, January 30, 2015 - 3:00pm
In this talk, we present an introduction to isogeometric analysis, a new methodology for solving partial differential equations (PDEs) based on a synthesis of computer aided design (CAD) and finite element analysis (FEA) technologies. In isogeometric analysis, the same geometric descriptions are used for the FEA and CAD models, and in this sense, the geometry is conserved throughout the design-through-analysis process. A prime motivation for the development of isogeometric analysis is to simplify the process of building detailed analysis models for complex engineering systems from CAD representations, a major bottleneck in the overall engineering process. However, we also demonstrate that isogeometric analysis is a powerful methodology for providing more accurate solutions of PDEs, and we summarize recently obtained mathematical results and describe open problems. We conclude by describing recent efforts which utilize the combined strengths isogeometric analysis and immersed boundary methods to tackle challenging problems arising in fluid dynamics, structural dynamics, and fluid-structure interaction.