author = {Liehr, Florian and Preusser, Tobias and Rumpf, Martin and Sauter,
	Stefan and Schwen, Lars Ole},
  title = {Composite Finite Elements for 3{D} Image Based Computing},
  journal = {Computing and Visualization in Science},
  year = {2009},
  volume = {12},
  pages = {171--188},
  number = {4},
  month = {April},
  abstract = {We present an algorithmical concept for modeling and simulation with
	partial differential equations (PDEs) in image based computing where
	the computational geometry is defined through previously segmented
	image data. Such problems occur in applications from biology and
	medicine where the underlying image data has been acquired through
	e. g. computed tomography (CT), magnetic resonance imaging (MRI)
	or electron microscopy (EM). Based on a level-set description of
	the computational domain, our approach is capable of automatically
	providing suitable composite finite element functions that resolve
	the complicated shapes in the medical/biological data set. It is
	efficient in the sense that the traversal of the grid (and thus assembling
	matrices for finite element computations) inherits the efficiency
	of uniform grids away from complicated structures. The method's efficiency
	heavily depends on precomputed lookup tables in the vicinity of the
	domain boundary or interface. A suitable multigrid method is used
	for an efficient solution of the systems of equations resulting from
	the composite finite element discretization. The paper focuses on
	both algorithmical and implementational details. Scalar and vector
	valued model problems as well as real applications underline the
	usability of our approach.},
  doi = {10.1007/s00791-008-0093-1},
  pdf = { 1}