On computing certain elements of the inverse of a sparse matrix
Communications of the ACM
Handbook for Automatic Computation: Linear Algebra (Grundlehren Der Mathematischen Wissenschaften, Vol 186)
SOI technology for the GHz era
IBM Journal of Research and Development
Beyond the conventional transistor
IBM Journal of Research and Development
A hybrid method for the parallel computation of Green's functions
Journal of Computational Physics
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Domain-Decomposition-Type Methods for Computing the Diagonal of a Matrix Inverse
SIAM Journal on Scientific Computing
Extension and optimization of the FIND algorithm: Computing Green's and less-than Green's functions
Journal of Computational Physics
A two-dimensional domain decomposition technique for the simulation of quantum-scale devices
Journal of Computational Physics
A fast algorithm for sparse matrix computations related to inversion
Journal of Computational Physics
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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An accurate and efficient algorithm, called fast inverse using nested dissection (FIND), for computing non-equilibrium Green's functions (NEGF) for nanoscale transistors has been developed and applied in the simulation of a novel dual-gate metal-oxide-semiconductor field-effect transistor (MOSFET) device structure. The method is based on the algorithm of nested dissection. A graph of the matrix is constructed and decomposed using a tree structure. An upward and downward traversal of the tree yields significant performance improvements for both the speed and memory requirements, compared to the current state-of-the-art recursive methods for NEGF. This algorithm is quite general and can be applied to any problem where certain entries of the inverse of a sparse matrix (e.g., its diagonal entries, the first row or column, etc.) need to be computed. As such it is applicable to the calculation of the Green's function of partial differential equations. FIND is applicable even when complex boundary conditions are used, for example non reflecting boundary conditions.