Sparsity structure and Gaussian elimination
ACM SIGNUM Newsletter
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
On computing certain elements of the inverse of a sparse matrix
Communications of the ACM
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Computing entries of the inverse of a sparse matrix using the FIND algorithm
Journal of Computational Physics
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)
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The central computation in atomistic, quantum transport simulation consists in solving the Schrödinger equation several thousand times with non-equilibrium Green's function (NEGF) equations. In the NEGF formalism, a numerical linear algebra problem is identified related to the computation of a sparse inverse subset of general sparse unsymmetric matrices. The computational challenge consists in computing all the diagonal entries of the Green's functions, which represent the inverse of the electron Hamiltonian matrix. Parallel upward and downward traversals of the elimination tree are used to perform these computations very efficiently and reduce the overall simulation time for realistic nanoelectronic devices. Extensive large-scale numerical experiments on the CRAY-XE6 Monte Rosa at the Swiss National Supercomputing Center and on the BG/Q at the Argonne Leadership Computing Facility are presented.