We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

Abstract. The dimer method is a Hessian-free algorithm for computing saddle points. We augment the method with a linesearch mechanism for automatic step size selection as well as preconditioning capabilities. We prove local linear convergence. A series of numerical tests demonstrate significant performance gains.

Abstract. Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. At the same time, this affects the accuracy of the computation. We analyze various approaches proposed for enhancement of the Lattice Boltzmann Methods (LBM) stability. In addition to the previously known methods, the Multiple Relaxation Time (MRT) models, the entropic lattice Boltzmann method (ELBM), and filtering (including entropic median filtering), we develop and analyze new filtering techniques with independent filtering of different modes.All these methods affect the dissipation in the system and may adversely affect the reproduction of the proper physics. To analyze the effect of dissipation on accuracy and to prepare practical recommendations, we test the enhanced LBM methods on the standard benchmark, the 2D lid driven cavity on a coarse grid (101×101 nodes). The accuracy was estimated by the position of the first Hopf bifurcation points in these systems.We find that two techniques, MRT and median filtering, succeed in yielding a reasonable value of the Reynolds number for the first bifurcation point. The newly created limiters, which filter the modes independently, also pick a reasonable value of the Reynolds number for the first bifurcation.1. Introduction. Lattice Boltzmann schemes are a type of discrete algorithm which can be used to simulate fluid dynamics and more [3,12,32]. One of the nicest properties of an LB scheme is that the transport component of the algorithm, advection, is exact. All of the dissipation in the discrete system then occurs due to the relaxation operation. This dissipation occurs at different orders of the small parameter, the time step [28]. The first order gives an approximation to the Navier Stokes equations (with some error terms due to the discrete velocity system). The higher orders include higher space derivatives, similarly to Burnett and super-Burnett type systems. (They differ from the Burnett and super-Burnett terms and may have better stability properties, see a simple case study for the Ehrenfests' collisions in [24]). The form of the dissipative terms in the macroscopic dynamics is driven by the form of the discrete equilibrium, the analogy to the Maxwell distribution, the coefficients of the dissipative terms are selected by the collision operator. In the standard and most basic relaxation operation, the single time BGK relaxation [4], these coefficients cannot be modified independently. One mechanism which is used to stabilize LB schemes is to generalize this to an MRT operator where these coefficients can be varied independently [16,17,13,14,15,25].An MRT relaxation operation involves selecting a new basis to perform relaxation in. This basis must necessarily include the macroscopic moments (which do not vary during relaxation) and also includes elements used to vary the hydrodynamic viscosity. Depending on the size of the velocity set a number of degrees of freedom may remain available. These degrees of freedom can be used to modify the coefficien...