author = {Nemitz, Oliver and Nielsen, Michael Bang and Rumpf, Martin and Whitaker,
  title = {Narrow Band Methods for {PDEs} on Very Large Implicit Surfaces},
  booktitle = {Vision, Modeling and Visualization},
  year = {2007},
  editor = {Lensch, Hendrik~P.~A. and Rosenhahn, Bodo and Seidel, Hans-Peter
	and Slusallek, Philipp and Weickert, Joachim},
  pages = {171--180},
  abstract = {Physical simulation on surfaces and various applications in geometry
	processing are based on partial differential equations on surfaces.
	The implicit representation of these eventually evolving surfaces
	in terms of level set methods leads to effective and flexible numerical
	tools. This paper addresses the computational problem of how to solve
	partial differential equations on level sets with an underlying very
	high-resolution discrete grid. These high-resolution grids are represented
	in a very efficient format, which stores only grid points in a thin
	narrow band. Reaction diffusion equations on a fixed surface and
	the evolution of a surface under curvature motion are considered
	as model problems. The proposed methods are based on a semi implicit
	finite element discretization directly on these thin narrow bands
	and allow for large time steps. To ensure this, suitable transparent
	boundary conditions are introduced on the boundary of the narrow
	band and the time discretization is based on a nested iteration scheme.
	Methods are provided to assemble finite element matrices and to apply
	matrix vector operators in a manner that do not incur additional
	overhead and give fast, cache-coherent access to very large data
  pdf = { 1},
  keywords = {MESHING, FEM, LEVELSET}