Advancingfront

Advancingfront, also known as the advancing-front method, is a family of unstructured mesh generation algorithms that construct meshes by incrementally advancing a front from a domain boundary into the interior. It is used to generate meshes for finite element analysis and related simulations in two and three dimensions, producing triangles or tetrahedra.

Starting from the boundary, the current front consists of boundary edges (2D) or faces (3D). At each step a front element is selected and a new vertex is placed inside the domain to form a new element with existing front edges. Placement follows a size function and quality constraints to avoid degenerate or poorly shaped elements, and the front is updated accordingly.

2D meshes yield triangles, 3D meshes yield tetrahedra. Front management and local refinement ensure conformance to curved boundaries and target element sizes.

Advantages include explicit boundary conformity and controlled element quality; it can adapt to heterogeneous size fields. Challenges involve robust front propagation in complex geometries and maintaining a valid front during aggressive refinements.

Originating in the late 1980s and 1990s as an approach to improve mesh quality, advancingfront remains one of the standard techniques for unstructured meshing and is frequently combined with smoothing or local optimization.