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The many faces of stiffness

Banff International Research Station for Mathematical Innovation and Discovery

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: (i) Textbook-type (decaying) numerical ODE stiffness (ii) Highly oscillatory stiffness (iii) Stiffness matrix (iv) Numerical stiffening. Some of these terms are popular in scientifc 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.

Mathematics; Numerical analysis; Partial differential equations; Scientific computing

video/mp4

Author affiliation: University of British Columbia

2020-12-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/76704

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/