An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculations, thus is makes accurate quantum transport calculations for large systems possible.

We present a novel linear scaling ab initio total energy electronic structure calculation method, which is simple to implement, easily to parallelize, and produces essentially the same results as the direct ab initio method, while it could be thousands of times faster.

We have carried out a survey of codes and algorithms used on NERSC computers within the science category of material science. This is part of the effort to track the usage of different algorithms in NERSC community. This survey is based on the data provided in the ERCAP application of FY06. To figure out the usage of each code in one account, we have multiplied the total high performance computer (HPC) time allocation (MPP hours) of this account with the percentage usage of this code as estimated by the users in the ERCAP application. This is not the actual usage time, but should be a good estimation of it, and it represents the intention of the users.

We present a new linearly scaling three-dimensional fragment (LS3DF) method for large scale ab initio electronic structure calculations. LS3DF is based on a divide-and-conquer approach, which incorporates a novel patching scheme that effectively cancels out the artificial boundary effects due to the subdivision of the system. As a consequence, the LS3DF program yields essentially the same results as direct density functional theory (DFT) calculations. The fragments of the LS3DF algorithm can be calculated separately with different groups of processors. This leads to almost perfect parallelization on tens of thousands of processors. After code optimization, we were able to achieve 35.1 Tflop/s, which is 39percent of the theoretical speed on 17,280 Cray XT4 processor cores. Our 13,824-atom ZnTeO alloy calculation runs 400 times faster than a direct DFT calculation, even presuming that the direct DFT calculation can scale well up to 17,280 processor cores. These results demonstrate the applicability of the LS3DF method to material simulations, the advantage of using linearly scaling algorithms over conventional O(N3) methods, and the potential for petascale computation using the LS3DF method.