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

Created from the Publication Database of the Vienna University of Technology.