Partial inverses of block tridiagonal non-Hermitian matrices

Abstract

The poster presents a parallel matrix inversion algorithm that has been implemented to be part of a matrix inverse library used by the SMEAGOL ab initio electronic code [1]. The SMEAGOL package uses a combination of Density Function Theory (DFT) and Non-Equilibrium Green's Functions (NEGF) to study nanoscale electronic transport under the effect of an applied bias potential. SMEAGOL is developed by the computational spintronics group in Trinity College, Dublin. Matrix inversion must be used in order to obtain the Green's function required by the SMEAGOL code. Efficient parallel scaling of the SMEAGOL code requires that the matrix inverse be calculated in parallel. In many cases, only the block tridiagonal part of inverse is needed. This algorithm provides the block tridiagonal subset of the inverse of a sparse non-Hermitian block tridiagonal matrix.