Related papers: Spatial pattern of discrete and ultradiscrete Gray…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
A cellular automaton that is a generalization of the box-ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: nonautonomous discrete KP lattice and…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
This paper deals with the numerical resolution of kinetic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. We focus on the kinetic model considered in [18, 17] where alignment is…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity $\epsilon$ of one of the two solution…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard…
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
Pattern separation is a computational process by which dissimilar neural patterns are generated from similar input patterns. We present an information-geometric formulation of pattern separation, where a pattern separator is modelled as a…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…