# Past Research

The LBNL Mathematics Group has made fundamental contributions to some of the key mathematical and algorithmic technologies in common practice and everyday use worldwide. These projects are lead by one of our four principle investigators: Alexandre Chorin, James A. Sethian, Jon Wilkening and Per-Olof Persson.

## X-FOSLS: Extended Finite Element Techniques for Crack Propagation and Fracture

“X-FOSLS” enhances standard finite elements to include the difficult and challenging cases in which singularities and pathologies in the solution cause standard techniques to fail. They rely on a consistent mathematical formulation of jump and internal boundary conditions, and are used in crack/fracture calculations and the analysis of the failure of interconnect lines in… Read More »

## Sub-Cell Shock Capturing using Artificial Viscosity

As above, finite element methods naturally work on unstructured meshes, and as such offer the chance to compute physics inside and around highly complex, and perhaps moving boundaries. However, they have traditionally been plagued by low order. A new set of sub-cell shock capturing, using cleverly chosen spectral viscosities, has led to a breakthrough approach for transonic/supersonic flow and Reynolds averaged turbulent… Read More »

## Moving Meshing Algorithms for Implicit Structures

DistMesh is a robust and reliable method for generating unstructured triangular and tetrahedral meshes, where the geometry is specified by implicit functions. DistMesh uses a Delaunay triangulation routine and tries to optimize the node locations by a force-based smoothing procedure. The topology is regularly updated by Delaunay, and boundary points are only allowed to move tangentially to the boundary by projections using the implicit function. The approach allows meshing of MRI/CT images and… Read More »