Related papers: Discrete gradient methods for port-Hamiltonian dif…
Computing gradients of a cost function is central to design-based optimization and machine learning algorithms. Equilibrium propagation provides an exact method to compute gradients in hardware by exploiting the inherent physical laws. The…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
In this paper, we focus on constructing numerical schemes preserving the averaged energy evolution law for nonlinear stochastic wave equations driven by multiplicative noise. We first apply the compact finite difference method and the…
This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This includes Riemannian…
This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…
We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and…
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
Port-Hamiltonian (pH) systems are a very important modeling tool in almost all areas of systems and control, in particular in network based model of multi-physics multi-scale systems. They lead to remarkably robust models that can be easily…
This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…
In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping. We focus on two particular examples, namely, the continuous-time ensemble Kalman-Bucy…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…