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 I decided to make some visual examples inspired by the unpublished textbook by Prof.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!”

Monthly Update — March 2020

Well, March was an interesting month. Between the COVID-19 pandemic shutting down BYU campus, transitioning to online classes, hitting the homestretch for classes, turning 31(!), and work obligations, I found some time to work through the orthoplanar spring problem in Coreform Flex and Crunch. Below is a video I captured of my first start-to-finish simulationContinue reading “Monthly Update — March 2020”

Monthly Update — Feb 2020

Coreform Short-Course In February, Coreform held its second short-course, which I attended. It was fairly similar to the last short-course, though a bit more polished. The biggest difference, however, was the unveiling of their beta version of Flex preprocessing software — which is built on the Trelis meshing software they obtained through their acquisition ofContinue reading “Monthly Update — Feb 2020”

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”

Monthly update – Jan 2020

January was a bit of a slow month – most of my thesis time was spent on building some exemplar CAD models and constructing example finite element meshes on them. I’ve sent the meshes to the rest of Dr. Scott’s research team to begin discussing maturity of their production code for handling the various volumetricContinue reading “Monthly update – Jan 2020”

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”

About the Blog

After graduating from RPI in 2012 I began working as a finite element analyst in support of my employer’s manufacturing mission. In 2016 I began investigating a flavor of the finite element method called isogeometric analysis (IGA), which eventually led to a full-fledged research project into the method. The project consisted primarily of a collaborationContinue reading “About the Blog”