Example PhD

Parallel Sparse Solvers for Computational Chemistry

Supervisor: Professor D.W. Walker

Keywords: Sparse linear algebra, pre-conditioners, computational chemistry.

Computational Chemistry is a compute-intensive application area that has direct relevance to the development of new energy relevant technologies including generation, storage, emissions and low carbon technologies. To address these critically important areas will require methods that can scale linearly with increasing number of atoms, so called O(N) methods. The main computational chemistry applications to be addressed in this project involve developing parallel strategies for a screened multiple-scattering (or Green’s function) approach. This leads to a sparse matrix representation where a serial version has been implemented enabling 1024 atoms on a single processor, and as a function of increasing number of atoms displays O(N) scaling. Previously, our collaborators have developed a Green’s function code based upon screened Korringa, Kohn, Rostoker (KKR) methods. This “scr-KKA-CPA” package handles the effects of substitutional disorder on an equal footing with the electronic structure using either the single-site coherent potential approximation (CPA) or the KKR dynamical cluster approximation to account for correlation beyond mean-field theories (single-site). The scr-KKR-CPA package allows for the simulation of system sizes ranging from tens of atoms to tens of thousands of atoms and is capable of treating a variety of boundary conditions. A key aspect of this approach is that it results in a sparse representation that scales linearly in both memory requirements and floating point operations as the number of atoms in the system. The sparse linear system can be solved using sparse non-symmetric preconditioned iterative methods and sparse direct methods using SuperLU. However, an appropriate preconditioner for use in the parallel algorithm is needed, and this is the main focus of this project. Thus, this project will investigate the performance of parallel preconditioners for the scr-KKR-CPA code, both from the point of view of scalability and numerical stability. The main aim is to make available to the computational chemistry community a parallel and numerically robust version of the scr-KKR-CPA code that is scalable on current and emerging multicore-based clusters.

Key Skills/Background: Open to Computer Science and computational chemistry graduates and postgraduates with good programming skills.

Contact: Professor D.W. Walker to discuss this research topic.