Fast algorithms for intersection of non-matching grids using Plücker coordinates

The XFEM and Mortar methods can be used in combination with non-matching or non-conforming grids to deal with problems on complex geometries. However the information about the mesh intersection must be provided. We present algorithms for intersections between 1d and 2d unstructured multi component simplicial meshes and their intersections with a background unstructured 3d mesh. A common algorithm based on the advancing front technique is used for the efficient selection of candidate pairs among simplicial elements. Bounding interval hierarchy (BIH) of axes aligned bounding boxes (AABB) of elements is used to initialize the front tracking algorithm. The family of element intersection algorithms is built upon a line-triangle intersection algorithm based on the Plücker coordinates. These algorithms combined with the advancing front technique can reuse the results of calculations performed on the neighboring elements and reduce the number of arithmetic operations. Barycentric coordinates on each of the intersecting elements are provided for every intersection point. Benchmarks of the element intersection algorithms are presented and three variants of the global intersection algorithm are compared on the meshes raising from hydrogeological applications.