@TechReport{	  it:2004-020,
  author	= {Malin Ljungberg and Krister {\AA}hlander},
  title		= {Generic Programming Aspects of Symmetry Exploiting
		  Numerical Software},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2004},
  number	= {2004-020},
  month		= may,
  note		= {To appear in the proceedings of the mini-symposium
		  ``Software Concepts and Free Software for PDEs'' of the
		  ECCOMAS 2004 congress, Jyv{\"a}skyl{\"a}, Finland, 24-28
		  July 2004},
  abstract	= {The use of the generalized Fourier transform as a means to
		  diagonalize certain types of equivariant matrices, and thus
		  speeding up the solution of numerical systems, is
		  discussed. Such matrices may arise in various applications
		  with geometrical symmetries, for example when the boundary
		  element method is used to solve an electrostatic problem in
		  the exterior of a symmetric object. The method is described
		  in detail for an object with a triangular symmetry, and the
		  feasibility of the method is confirmed by numerical
		  experiments.
		  
		  The design of numerical software for this kind of
		  applications is a challenge. It is argued that generic
		  programming is very suitable in this context, mainly
		  because it is type safe and promotes polymorphism
		  capabilities in link time.
		  
		  A generic C++ design of important mathematical abstractions
		  such as groups, vector spaces, and group algebras, is
		  outlined, illustrating the potential provided by generative
		  programming techniques. The integration of explicit support
		  for various data layouts for efficiency tuning purposes is
		  discussed. }
}