index

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

GPU Acceleration of femto library

On writing/optimizing CUDA kernels for a Finite Element library

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.

Introduction to SIMD Programming

Slides from a presentation describing how to improve CPU performance through vectorization

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.

Accelerating Mathematica with C++ libraries

How to speed up Mathematica notebooks by calling through to functions in C++ libraries

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.

Improving MFEM's CUDA Kernel Implementation

This document demonstrates how in some cases, eliminating template parameters can significantly reduce compile time and binary size, while retaining performance parity.

Setting up a Local Compiler Explorer

Compiler Explorer is a great tool for prototyping and understanding code snippets, and running a local instance can make it even more flexible and responsive.

CMake ExternalData Example

CMake's ExternalData provides a way for projects to download large data files just-in-time, rather than putting them directly in a git repo or project tarball. This feature doesn't seem to be used very often, so this is an example project showing how to set it up.