Algoim is a collection of high-order accurate numerical methods and C++ algorithms for working with implicitly defined geometry and level set methods. Motivated by multi-phase multi-physics applications, particularly those with evolving dynamic interfaces, these algorithms target core, fundamental techniques in level set methods. They have been designed with a view to standard finite difference implementations as well as more advanced finite element and discontinuos Galerkin implementations, multi-threading and massively parallel MPI computation. The collection includes high-order accurate quadrature algorithms for implicitly defined domains in hyperrectangles (such as for computing integrals on curved surfaces), Voronoi implicit interface methods for multi-phase interconnected interface dynamics, high-order accurate closest point calculations, accurate level set reinitialization and extension velocity schemes, and k-d trees optimized for codimension-one point clouds.
Usage and applications: Algoim-based algorithms have been used in a variety of high-order accurate computational physics applications, 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 have been coupled to high-order accurate implicit mesh discontinuous Galerkin methods and interfacial gauge methods. Ongoing applications include DOE HPC4Mfg projects on the modeling of rotary bell atomization, involving intricate interface dynamics and the generation of thousands of micrometer droplets in high performance peta-scale computation. In addition, the quadrature algorithms have found success in a number of worldwide research projects on solving PDEs on curved surfaces, extended finite element methods, and cut cell finite volume methods in computational physics, chemistry, and materials.