### Friday, June 5

## IP9

Quadratic Functionals and Integral Equations for Harmonic Wave Equations in Exterior Domains

8:00 AM-8:45 AM

*Chair: Graeme Fairweather, Colorado School of Mines*

*Room 246*

Harmonic linear wave equations in exterior domains may model the scattering and propagation of pressure waves, electromagnetic waves or elastodynamic waves. They lead to a large fields of application, including radar cross section calculations.

Using the out-going fundamental solution, integral equations reduce the exterior problem to a problem posed on the boundary of the scattering obstacle. After discretisation one obtains a complex matrix which is classically directly inverted.

In this lecture, the speaker will introduce a "natural" quadratic function that reaches its minimum in the space of all out-going and in-going solutions at the solution of the model exterior problem. Eliminating the singularities, a new mixed real integral system results. The discrete problem is solved using standard iterative algorithms such a the real conjugate gradient method and the Jacobi algorithm.

**Bruno Despres**

*DCSA/MLS, CEA-CELV, France*

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*tjf, 12/23/97*