ABSTRACT
R. GLOWINSKI University of Houston, Houston, Texas 77204-3476 , U . S .A . , Uni versity of Paris 6 and CERFACS, Toulouse, France
J . PERIAUX Dassault Aviation , 78 , quai M. Dassault 92214 , Saint-Cloud, France
Abstract . In this paper, we discuss a new method for solving the Helmholtz equation from Acoustics and two-dimensional Electro-Magnetics . The key idea of the method is to go back to the original wave equation and look for time periodic solutions . The methodology is essentially based on a shooting/least squares formulation in appropriate Hilbert spaces ; it is closely related to exact controllability and to the Hilbert Unique ness Method (H.U .M. ) of J . L. Lions . The resulting minimisation problem is solved by a preconditioned conjugate gradient algorithm which has quite good convergence properties . We introduce absorbing boundary conditions on the artificial boundary.
