Artificial boundary conditions for axisymmetric eddy current probe problems

Artificial boundary conditions for axisymmetric eddy current probe problems

We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann (DtN) map is proposed and mathematically justified via the analysis of a nonselfadjoint spectral problem. We rely of results from the spectral theory of compact perturbations of selfadjo...

Standard Flaws for Eddy Current Probe

Calibration procedures for eddy current inspections often involve the use of artifact standards containing manufactured flaws. The manufactured flaw is assumed to be a good approximation of the type of flaw being sought during the inspection. These manufactured flaws are most often produced by electrical dis charge machining (EDM) , milling, or the controlled growth of fatigue cracks. With simp...

Symmetric Coupling for Eddy Current Problems

Singularities of eddy current problems

We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of BOSSAVIT [11]. We describe the singularities of the solu...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...