Related papers: Initialisation from lattice Boltzmann to multi-ste…
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively…
We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…
We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow…
Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are…
Switching-constrained optimization problems form a difficult class of mathematical programs since their feasible set is almost disconnected while standard constraint qualifications are likely to fail at several feasible points. That is why…
In this paper, a lattice Boltzmann model with the single-relaxation-time model for the Cahn-Hilliard equation (CHE) is proposed. The discrete source term is redesigned through a third-order Chapman-Enskog analysis. By coupling the…
Lattice Boltzmann methods are a popular mesoscopic alternative to macroscopic computational fluid dynamics solvers. Many variants have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to…
We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability…
The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its…
A new homogenization approach for the simulation of multi-phase flows in heterogeneous porous media is presented. It is based on the lattice Boltzmann method and combines the grayscale with the multi-component Shan-Chen method. Thus, it…
Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in…
In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be…
Multi-component lattice Boltzmann models operating in a wide range of fluid viscosity values are developed and examined. The algorithm is constructed with the goal to enable engineering applications without sacrificing simplicity and…
Solving flow-related inverse problems such as topology optimization problems is intricate but significant in various engineering fields. The lattice Boltzmann method (LBM) and the related adjoint method are highly suitable to perform…
We show that the asymptotic properties of the link-wise artificial compressibility method are not compatible with a correct approximation of fluid properties. We propose to adapt the previous method through a framework suggested by the…
Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…
Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gowdy space-times. The simple objective of this paper is to…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it…
The Barzilai-Borwein (BB) method is a popular and efficient tool for solving large-scale unconstrained optimization problems. Its search direction is the same as for the steepest descent (Cauchy) method, but its stepsize rule is different.…