@TechReport{	  it:2010-010,
  author	= {Maya Neytcheva and Erik B{\"a}ngtsson and Elisabeth
		  Linn{\'e}r},
  title		= {Finite-Element Based Sparse Approximate Inverses for
		  Block-Factorized Preconditioners},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2010},
  number	= {2010-010},
  month		= mar,
  abstract	= {In this work we analyse a method to construct a
		  numerically efficient and computationally cheap sparse
		  approximations of some of the matrix blocks arising in the
		  block-factorised preconditioners for matrices with a
		  two-by-two block structure. The matrices arise from finite
		  element discretizations of partial differential equations.
		  We consider scalar elliptic problems, however the approach
		  is appropriate for other types of problems such as
		  parabolic or systems of equations.
		  
		  The technique is applicable for both selfadjoint and
		  non-selfadjoint problems, in two as well as in three
		  dimensions. We analyze in detail the 2D case and provide
		  extensive numerical evidence for the efficiency of the
		  proposed matrix approximations, both serial and parallel.}
}