论文信息 - Numerical Simulation of High Frequency Scattering Waves Using Exact Controllability Methods

Numerical Simulation of High Frequency Scattering Waves Using Exact Controllability Methods

The main goal of this article is to introduce a novel method for solving the Helmholtz equations 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. In order to find these last solutions we essentially use a least squares/shooting method which is closely related to exact controllability and to the Hilbert Uniqueness Method (HUM) of J. L. Lions. From this formulation and by analogy with other controllability problems we derive a conjugate gradient algorithm (in an appropriate Hilbert space) which has quite good convergence properties. Numerical experiments concerning the scattering of planar waves by convex or nonconvex obstacles show the efficiency of the new algorithm, particularly for air intake-like reflectors.

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