The words "stiff'', "stiffness'', "stiffening", etc., arise often in applications when simulating, calibrating and controlling dynamics. But these words often have different meanings in different contexts.
A subset on which we will concentrate includes:
- Textbook-type (decaying) numerical ODE stiffness
- Highly oscillatory stiffness
- Stiffness matrix
- Numerical stiffening
Some of these terms are popular in scientific computing, while others come from mechanical engineering. A potential confusion may arise in this way, and it gets serious when more than one meaning is encountered in the context of one application. Such is the case with the simulation of deformable objects in visual computing, where all of the above appear in one way or another under one roof.
In this lecture I will describe the meaning of stiffness in each of these topics, how they arise, how they are related, what practical challenges they bring up, and how these challenges are handled in context. The concepts and their evolution will be demonstrated.
It is about meshes -- their resolution and spectral properties -- both in time and in space.
*Texto informado pelo autor.
Uri M. Ascher is Professor of Computer Science at the University of British Columbia, Vancouver, Canada. He obtained his BSc and MSc in Applied Mathematics from Tel-Aviv University in 1969 and 1971, and his PhD in Computer Science from the University of Minnesota in 1975. He is a SIAM Fellow and recipient of CAIMS Research Prize. The focus of his work is on the investigation, promotion and application of novel, efficient and reliable methods in scientific computation, and their application in computer graphics, imaging and other approximation problems involving differential equations with constraints and optimization.