Numerical Analysis and Scientific Computing Seminar | David Williams, Current Challenges for Space-Time Finite Element Methods

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

David Williams, Assistant Professor, Department of Mechanical Engineering, Penn State University

Title

Current Challenges for Space-Time Finite Element Methods

Abstract

Space-time finite element methods (FEMs) are likely to grow in popularity due to the ongoing growth in the size, speed, and parallelism of modern computing platforms. The allure of space-time FEMs is both intuitive and practical. From the intuitive standpoint, there is considerable elegance and simplicity in accommodating both space and time using the same numerical discretization strategy. From the practical standpoint, there are considerable advantages in efficiency and accuracy that can be gained from space-time mesh adaptation: i.e. adapting the mesh in both space and time to resolve important solution features. However, despite these considerable advantages, there are numerous challenges that must be overcome before space-time FEMs can realize their full potential. These challenges are primarily associated with four-dimensional geometric obstacles (hypersurface and hypervolume mesh generation), four-dimensional approximation theory (basis functions and quadrature rules), four-dimensional boundary condition enforcement (well-posed, moving boundary conditions), and iterative-solution techniques for large-scale linear systems. In this presentation, we will provide a brief overview of space-time FEMs, and discuss some of the latest research developments and ongoing issues.