相关论文: Optimal artificial boundary conditions based on se…

We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…

Outside the core of the plasma, the plasma current and pressure rapidly transition to zero in a scrape-off or edge region or plasma-vacuum interface. However, existing tools for fixed-boundary magnetohydrodynamic equilibria in 2D and 3D…

Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…

We give a general family of electromagnetic boundary conditions applicable to arbitrary space--time interfaces between electromagnetic media, which include the known space--only and time--only boundary conditions as special cases. These…

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control…

We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems…

Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…

We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…

Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of…

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…

We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…

The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov -…

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…

The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with…

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…