相关论文: Structure-Preserving Optimal Control of Maxwell's …

This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…

We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian…

This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for dielectric inhomogeneity. Solving the steady-state modified PNP…

This paper focuses on the discrete-time backward stochastic linear quadratic (BSLQ) optimal control problem with nonhomogeneous system terms and cost function cross terms. The terminal constraint of such systems distinguishes it from…

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…

In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…

Reformulating the incompressible Stokes equations with the velocity sought in H(curl) has recently emerged as a promising approach for the design of helicity-preserving schemes in magnetohydrodynamics and pressure-robust finite element…

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…

A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's…

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…

In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations, namely for $\mathbf{H}(\mathbf{curl})$…

This paper analyzes the stability of optimal policies in the long-run stochastic control framework with an averaged risk-sensitive criterion for discrete-time MDPs on finite state-action space. In particular, we study the robustness of…

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…

In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that…

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a…

Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…

Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…

In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…