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Computing entries of the inverse of a sparse matrix using the FIND algorithm
Song Li
,
Shaikh S. Ahmed
,
Gerhard Klimeck
,
Eric Darve
Published
2008
in
J. Comput. Physics
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Abstract
Article history: Received 17 April 2007 Received in revised form 27 May 2008 Accepted 23 June 2008 Available online 17 July 2008 PACS: 02.60.Dc 02.70. c 73.23. b 73.63. b
Topics
Sparse matrix
Algorithm
Sparse matrix
Algorithm
Sparse matrix
Algorithm
55 Figures and Tables
Fig. 2. The model of a widely-studied double-gate SOI MOSFET with ultra-thin intrinsic channel. Typical values of key device parameters are also shown.
Fig. 3. bounda
Fig. 7. The mesh and its partitions. C1 =M.
Fig. 8. Examples of augmented trees.
Fig. 10. Merging clusters below level L.
Fig. 11. Merging rectangular clusters. Two Nx W clusters merge into an Nx 2W cluster.
Fig. 12. Partitioning of clusters above level L.
Fig. 13. Partitioning of clusters below level L.
Fig. 14. Density-of-states (DOS) and electron density plots from RGF and FIND.
Fig. 15. Comparison of the running time of FIND and RGF when Nx is fixed.
Fig. 16. Comparison of the running time between FIND and RGF when Ny is fixed.
Fig. 2. The model of a widely-studied double-gate SOI MOSFET with ultra-thin intrinsic channel. Typical values of key device parameters are also shown.
Fig. 3. bounda
Fig. 7. The mesh and its partitions. C1 =M.
Fig. 8. Examples of augmented trees.
Fig. 10. Merging clusters below level L.
Fig. 11. Merging rectangular clusters. Two Nx W clusters merge into an Nx 2W cluster.
Fig. 12. Partitioning of clusters above level L.
Fig. 13. Partitioning of clusters below level L.
Fig. 14. Density-of-states (DOS) and electron density plots from RGF and FIND.
Fig. 15. Comparison of the running time of FIND and RGF when Nx is fixed.
Fig. 16. Comparison of the running time between FIND and RGF when Ny is fixed.
Fig. 2. The model of a widely-studied double-gate SOI MOSFET with ultra-thin intrinsic channel. Typical values of key device parameters are also shown.
Fig. 3. bounda
Fig. 7. The mesh and its partitions. C1 =M.
Fig. 8. Examples of augmented trees.
Fig. 10. Merging clusters below level L.
Fig. 11. Merging rectangular clusters. Two Nx W clusters merge into an Nx 2W cluster.
Fig. 12. Partitioning of clusters above level L.
Fig. 13. Partitioning of clusters below level L.
Fig. 14. Density-of-states (DOS) and electron density plots from RGF and FIND.
Fig. 15. Comparison of the running time of FIND and RGF when Nx is fixed.
Fig. 16. Comparison of the running time between FIND and RGF when Ny is fixed.
Fig. 2. The model of a widely-studied double-gate SOI MOSFET with ultra-thin intrinsic channel. Typical values of key device parameters are also shown.
Fig. 3. bounda
Fig. 7. The mesh and its partitions. C1 =M.
Fig. 8. Examples of augmented trees.
Fig. 10. Merging clusters below level L.
Fig. 11. Merging rectangular clusters. Two Nx W clusters merge into an Nx 2W cluster.
Fig. 12. Partitioning of clusters above level L.
Fig. 13. Partitioning of clusters below level L.
Fig. 14. Density-of-states (DOS) and electron density plots from RGF and FIND.
Fig. 15. Comparison of the running time of FIND and RGF when Nx is fixed.
Fig. 16. Comparison of the running time between FIND and RGF when Ny is fixed.
Fig. 2. The model of a widely-studied double-gate SOI MOSFET with ultra-thin intrinsic channel. Typical values of key device parameters are also shown.
Fig. 3. bounda
Fig. 7. The mesh and its partitions. C1 =M.
Fig. 8. Examples of augmented trees.
Fig. 10. Merging clusters below level L.
Fig. 11. Merging rectangular clusters. Two Nx W clusters merge into an Nx 2W cluster.
Fig. 12. Partitioning of clusters above level L.
Fig. 13. Partitioning of clusters below level L.
Fig. 14. Density-of-states (DOS) and electron density plots from RGF and FIND.
Fig. 15. Comparison of the running time of FIND and RGF when Nx is fixed.
Fig. 16. Comparison of the running time between FIND and RGF when Ny is fixed.
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