Novel linear algebraic theory and one-hundred-million-atom quantum material simulations on the K computer
Takeo Hoshi · 2014
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations.The algorithms are Krylov-subspace (iterative) solvers for generalized shifted linear equations, in the form of (zS-H)x x x = b b b, in stead of conventional generalized eigen-value equation.The method was implemented in our order-N calculation code ELSES (http://www.elses.jp/)with modelled systems based on ab initio calculations.The code realized one-hundred-million-atom, or 100-nm-scale, quantum material simulations on the K computer in a high parallel efficiency with up to all the built-in processor cores.The present paper also explains several methodological aspects, such as use of XML files and 'novice' mode for general users.A sparse matrix data library in our real problems ( http://www.elses.jp/matrix/ ) was prepared.Internal eigen-value problem is discussed as a general need from the quantum material simulation.The present study is a interdisciplinary one and is sometimes called 'Application-Algorithm-Architecture co-design'.The co-design will play a crucial role in exa-scale scientific computations.