Sum Factorization in FEM
A description of the sum factorization trick for finite elements and the conditions for when it can be used effectively.
Parameterized Shape Optimization
How to approximate the derivative of mesh-generation when explicitly parameterizing designs through level set functions
Algorithmic Differentiation on Graphs
An overview of how to use graphs to implement forward and reverse mode differentiation.
Packing Conductive Particles with DEM
Simulation of packing spherical conductive particles and calculating effective resistance.
Smoothed Constructive Solid Geometry Operations
On combining primitive shapes with smoothed boolean operations, and how to mitigate some of the problems that arise.
Making Meshes from Level Set Functions
An overview of the "universal mesh" algorithm for creating quality simplex meshes of implicitly-defined regions.
Triply-Periodic Surfaces
A reference containing information about periodic surfaces suitable for infill structure in 3D printed parts.
Stability of constrained Newmark-beta
Different methods of enforcing simple constraints on ODEs can impose additional stability criteria.
Multigrid on Unstructured Meshes
This document investigates the effectiveness of multigrid when used on a nonconforming hierarchy of unstructured meshes.
Mesh Coarsening
An algorithm for coarsening simplex meshes, to enable multigrid methods with unstructured meshes.
Mesh Vertex Relaxation
A simple iterative procedure for improving element quality of finite element meshes.
Visual Proof: Sum of Squares
Gauss is said to have found an elegant visual proof for summing integers. Does a similar idea work for summing perfect squares?
Coffee Cup Vibrations
What sound does a coffee mug make when you tap it with a spoon? In this post, we write a small 2D finite element code in Mathematica to simulate a coffee cup vibrating.