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Section: New Results

Keywords : Helmholtz Equation, Oscillated Polynomials, Lagrange Multipliers.

New mixed hybrid elements combining Lagrange polynomials and plane waves for the solution of the Helmholtz equation

Participants : Mohamed Amara, Hélène Barucq, Rabia Djellouli.

We propose a new mixed-hybrid-type solution methodology to be applied for solving high-frequency Helmholtz problems. The proposed approach distinguishes itself from similar methods by a local approximation of the solution with oscillated finite elements polynomials satisfying the wave equation. The weak continuity of the solution across the element interfaces is enforced using Lagrange multipliers. A convergence analysis of the method has been performed an it shows the strong stability properties of this new discretization. Numerical results obtained in the case of two-dimensional waveguide problems illustrate the computational efficiency of the proposed solution methodology. Now, we are applying the new finite element method for solving the seismic wave equation.


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