On some imbedding methods applied to fluid dynamics and elecjro-magnetics

A Spectral Embedding Method Applied to the Advection–Diffusion Equation

“…have been applied to different kinds of in Section 3, concerning the Fourier analysis, and in Section PDE, such as linear elliptic equations but, also, in fluid 4, concerning the boundary element approach. Finally, in dynamics to the Euler or Navier-Stokes equations, or in Section 5, we produce some numerical tests in order to electromagnetism to the Maxwell equations [5][6][7]. To our give measurements of the accuracy of the method and to knowledge, the closest approaches to the one described in outline its capabilities.…”

“…Let us recall that the basic idea is to solve a given partial The paper is composed of four main parts (Sections differential equation (PDE) in a simple cartesian domain [2][3][4][5]. In Section 2 we present the basic principles of the Ͷ in which the complex domain ⍀ is embedded.…”

Fictitious domain/mixed finite element approach for a class of optimal shape design problems

“…Fictitious domam methods or domain imbedding methods have recently become a subject of mcreasing interest, see for instance [1] The obvious reason is that they allow to obtam numencal solutions to problems of complicated geometry by operatmg on a simple geometry domain containing the complicated one The use of fictitious domain methods in shape optimization is particularly attractive because of the special features of the problem. In the classical approach to shape optimization, ï.e.…”

A moving mesh fictitious domain approach for shape optimization problems

“…This can be accomplished in several ways. The following functional analytic fictitious domain methods have been studied mostly by the French school led by Glowinski: In the optimal control approach [2,27], the problem is formulated as a distributed optimal control problem. Another possibility is to add some constraints to the extended problem.…”