@TechReport{	  it:2011-025,
  author	= {Martin Kronbichler and Katharina Kormann},
  title		= {A Generic Interface for Parallel Cell-Based Finite Element
		  Operator Application},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2011},
  number	= {2011-025},
  month		= nov,
  abstract	= {We present a memory-efficient and parallel framework for
		  finite element operator application implemented in the
		  generic open-source library deal.II. Instead of assembling
		  a sparse matrix and using it for matrix-vector products,
		  the operation is applied by cell-wise quadrature. The
		  evaluation of shape functions is implemented with a
		  sum-factorization approach. Our implementation is
		  parallelized on three levels to exploit modern
		  supercomputer architecture in an optimal way: MPI over
		  remote nodes, thread parallelization with dynamic task
		  scheduling within the nodes, and explicit vectorization for
		  utilizing processors' vector units. Special data structures
		  are designed for high performance and to keep the memory
		  requirements to a minimum. The framework handles adaptively
		  refined meshes and systems of partial differential
		  equations. We provide performance tests for both linear and
		  nonlinear PDEs which show that our cell-based
		  implementation is faster than sparse matrix-vector products
		  for polynomial order two and higher on hexahedral elements
		  and yields ten times higher Gflops rates.}
}