In this paper we analyze a Galerkin procedure, based on a combination of finite and spectral elements, for approximating a time-harmonic acoustic wave scattered by a bounded inhomogeneity. The finite element method used to approximate the near field in the region of inhomogeneity is coupled with a nonlocal boundary condition, which consists in a linear… (More)

In applications related to electrical power engineering, the displacement current existing in a metallic conductor is negligible compared with the conduction current. In such situations, the displacement currents may be dropped from Maxwell’s equations and one obtains a magneto-quasistatic sub-model usually called the eddy current problem. The eddy current… (More)

In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderón projector to obtain a symmetric coupled system,… (More)

We consider the problem of detecting bounded inhomogeneous obstacles in an infinite tubular waveguide. We have in mind the application of acoustic techniques to inspect underground pipes such as sewers: In this application a loud-speaker and microphone are lowered into a man-hole. Sound pulses are created in the pipe, and the acoustic field reflected by… (More)

We propose a proof of existence of solutions which is conceptually simpler than the previous proof in [1]. Indeed, our proof is based on a direct parabolic regularization of the problem, whereas previous proofs involved a change of unknowns rendering the problem to a parabolic-hyperbolic formulation. Moreover, we believe that our approach also gives a way… (More)