Mappings, Inversion, and Basis Functions… Oh my!

I recently had some discussions with some coworkers and fellow graduate students and felt a bit lacking in my explanations regarding element inversion and the difference between interpolatory and non-interpolatory basis functions. I decided to make some visual examples inspired by the unpublished textbook by Prof. Carlos Felippa and thought I’d share some thoughts inContinue reading “Mappings, Inversion, and Basis Functions… Oh my!”

Gauss Quadrature

It seems to me that many practitioners of finite elements are engineers (myself included), as opposed to mathematicians. Part of the mythos of finite elements is Gauss quadrature. We see its name thrown around when discussing integration in finite elements, and we know that it is an efficient scheme. But us engineers don’t necessarily knowContinue reading “Gauss Quadrature”

Bézier Extraction

Perhaps the most important concept to understand in smooth-spline FEA is called Bézier Extraction – extraction of the piecewise Bézier elements (composed of Bernstein polynomials) that constitute a basis-spline (aka B-spline). One can actually extract any arbitrary family of piecewise elements (e.g. Lagrange), but we’ll cover that in a future post. The Bézier extraction processContinue reading “Bézier Extraction”