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K. Rupp, A. Jüngel, T. Grasser:
"Matrix Compression for Spherical Harmonics Expansions of the Boltzmann Transport Equation for Semiconductors";
in: "ASC Report 10/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2, 1 - 32.

We investigate the numerical approximation of the semiconductor Boltzmann
transport equation using an expansion of the distribution function in spherical
harmonics. A complexity analysis shows that traditional implementations
of higher order spherical harmonics expansions suffer from huge memory requirements,
especially for two and three dimensional devices. To overcome
these complexity limitations, a compressed matrix storage scheme using Kronecker
products is proposed, which reduces the memory requirements for the
storage of the system matrix significantly. Furthermore, the total memory
requirements are asymptotically dominated only by the memory required for
the unknowns. We discuss the increased importance of the selection of an
appropriate linear solver and show that execution times for matrix-vector
multiplications using the compressed matrix scheme are even smaller than
those for an uncompressed system matrix. Numerical results demonstrate
the applicability of our method and confirm our theoretical results.

Boltzmann equation, Spherical Harmonics, Kronecker product

http://www.asc.tuwien.ac.at/preprint/2010/asc10x2010.pdf