On combining primitive shapes with smoothed boolean operations, and how to mitigate some of the problems that arise.

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.