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The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…

Optimization and Control · Mathematics 2022-09-14 Denis Khimin , Marc C. Steinbach , Thomas Wick

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

Structure-preserving methods can be derived for the Vlasov-Maxwell system from a discretisation of the Poisson bracket with compatible finite-elements for the fields and a particle representation of the distribution function. These…

Numerical Analysis · Mathematics 2021-11-17 Benedikt Perse , Katharina Kormann , Eric Sonnendrücker

The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…

Numerical Analysis · Mathematics 2023-05-10 Omkar H. Ramachandran , Leo C. Kempel , John Luginsland , B. Shanker

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

Probability · Mathematics 2008-12-20 Seid Bahlali

We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with…

Analysis of PDEs · Mathematics 2025-04-02 Hoai Minh Nguyen , Swarnendu Sil

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

Optimization and Control · Mathematics 2026-03-27 Jingwei Chen , Jun Ye , Feng Chen

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

Numerical Analysis · Mathematics 2020-03-23 Marcella Bonazzoli , Victorita Dolean , Ivan G. Graham , Euan A. Spence , Pierre-Henri Tournier

In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schr\"{o}dinger equations in the Coulomb gauge. We first prove the global existence of weak solutions to the equations. Next we propose an…

Numerical Analysis · Mathematics 2017-03-08 Chupeng Ma , Liqun Cao , Jizu Huang , Yanping Lin

In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability, for cases of typical…

Numerical Analysis · Mathematics 2017-04-26 Adérito Araújo , Sílvia Barbeiro , Maryam Khaksar Ghalati

Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a…

Numerical Analysis · Mathematics 2025-10-17 Leon Herles , Mario Mally , Jörg Ostrowski , Sebastian Schöps , Melina Merkel

In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in a variational energy sense), and is maximum bound…

Numerical Analysis · Mathematics 2022-01-05 Hong-lin Liao , Tao Tang , Tao Zhou

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…

Computational Physics · Physics 2025-12-05 Christopher DeGrendele , Nguyen Ly , Francois Cadieux , Michael Barad , Dongwook Lee , Jared Duensing

We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which…

Numerical Analysis · Mathematics 2024-08-02 Aaron Brunk , Herbert Egger , Oliver Habrich

We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein-Taylor model. In the diffusive scaling this model is a hyperbolic approximation to the heat equation. We…

Numerical Analysis · Mathematics 2013-08-05 Giacomo Albi , Michael Herty , Christian Jörres , Lorenzo Pareschi

We analyze, in two dimensions, an optimal control problem for the Navier--Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular…

Optimization and Control · Mathematics 2022-08-19 Francisco Fuica , Felipe Lepe , Enrique Otarola , Daniel Quero

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…

Optimization and Control · Mathematics 2012-04-30 C. M. Campos , O. Junge , S. Ober-Blöbaum

The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…

Numerical Analysis · Mathematics 2023-12-21 Eric Lindström , Larisa Beilina

This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…

Analysis of PDEs · Mathematics 2015-06-12 Michael Hintermüller , Tobias Keil , Donat Wegner