Friday, June 5

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

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tjf, 12/23/97