THOMAS YOUNG CENTRE:
THE LONDON CENTRE FOR THEORY AND SIMULATION OF MATERIALS
Dr Peter Haynes (Imperial College)
It is 20 years since Yang proposed the first "divide-and-conquer" linear-scaling method [1]. Since then a great deal of effort has been invested in the development of O(N) methods but there is relatively little to show for it in terms of practical applications. In this talk I will suggest why this is the case and how it may be addressed.
First, I will briefly outline the scheme implemented in the ONETEP code [2], focussing on the in situ optimisation of local orbitals that enables plane-wave accuracy to be achieved.
Second, I will present results of simulations of polar semiconductor nanorods that are amenable to O(N) methods and demonstrate the sorts of questions and systems that can be addressed. Finally I will present recent work on the optimisation of an additional set of local orbitals for unoccupied states that allow the calculation of optical absorption spectra and open up the way for future developments.
[1] Phys. Rev. Lett. 66, 1438 (1991)
[2] www.onetep.org
Our chemical natural intuition suggests that the numerical effort required for the calculation of a big system should be proportional to its size.
Algorithms that allow us to do electronic structure calculations with linear scaling, so-called O(N) algorithms, have been developed and are now well established even though they are not yet widely used.
In this talk I will discuss the physical foundations that allow us to obtain linear scaling and outline the basic ideas of several O(N) algorithms. Finally I will briefly describe our efforts to develop an O(N) density functional code using a wavelet basis set.