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PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages

Fredi Tröltzsch, Irwin Yousept (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages

Fredi Tröltzsch, Irwin Yousept (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x ∈ ℝ N where g is a continuous function, nondecreasing w.r.t. u . We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations....

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x ∈ ℝ N where g is a continuous function, nondecreasing w.r.t. u. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations. ...

Poisson-Boltzmann equation in ℝ³

A. Krzywicki, T. Nadzieja (1991)

Annales Polonici Mathematici

The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, u | ∂ Ω = 0 . One studies the existence of a solution of the problem and its properties.

Propagation of electromagnetic waves in non-homogeneous media

Radjesvarane Alexandre, Hassan Taha (2004)

Applications of Mathematics

We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.

Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems

Chang-Ho Song, Yong-Gon Ri, Cholmin Sin (2022)

Applications of Mathematics

In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence...

Proposition de préconditionneurs pseudo-différentiels pour l’équation CFIE de l’électromagnétisme

David P. Levadoux (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a weak parametrix of the operator of the CFIE equation. An interesting feature of this parametrix is that it is compatible with different discretization strategies and hence allows for the construction of efficient preconditioners dedicated to the CFIE. Furthermore, one shows that the underlying operator of the CFIE verifies an uniform discrete Inf-Sup condition which allows to predict an original convergence result of the numerical solution of the CFIE to the exact one.

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