Code
I develop and mantain Algoim, a collection of high-order accurate numerical methods and C++ algorithms for working with implicitly-defined geometry and level set methods, available on GitHub:
Algoim — https://algoim.github.io/
It includes:
- High-order accurate quadrature algorithms for computing integrals over implicitly-defined domains. Two different approaches are provided:
- Quadrature methods for domains implicitly-defined by a single level set function (sufficiently-smooth, but otherwise arbitrary); and
- Quadrature methods for multi-component domains implicitly-defined by multivariate polynomials, handling complex geometry such as multiple high-curvature pieces, junctions, self-intersections, and cusps.
- High-order accurate algorithms for computing closest points on implicitly-defined surfaces, with application to high-order level set reinitialisation and extension velocity schemes.
- k-d trees optimised for codimension-one point clouds.
Algoim-based algorithms have been used across much of my research in high-order multi-scale multi-physics modeling, including complex flow in non-trivial geometry, free surface flow driven by intricate surface tension dynamics, multi-scale models of thin-film foam dynamics, multi-phase fluid flow, and petascale simulation of rotary bell atomisation dynamics.
Algoim methods have also been implemented in a variety of projects around the world, including LBNL's AMReX, LLNL's MFEM, deal.II, and BoSSS, as well as cutting edge research on immersed and extended finite element methods and cut cell finite volume methods in computational physics, chemistry, and materials.