Stabilized Hybrid and Mixed Finite Element Methods for Helmholtz Problems

Abstract eng:
Stabilized hybrid and mixed finite element methods are proposed for solving Helmholtz problems in heterogeneous media. The methods are based on a hybridized dual mixed formulation in velocity (flux) and pressure fields stabilized by adding least squares residual of the governed equations. The local problems, in the velocity and pressure fields, are solved at element level to eliminate these variables in favor of the Lagrange multipliers, identified as the trace of the pressure on the element edges of the finite element mesh. A global system is assembled involving only the degrees of freedom associated with the Lagrange multipliers as usually in Hybrid methods. Polynomial bases are adopted to approximate the global problem in the Lagrange multipliers. Polynomial or special bases, such as plane-wave bases, can be also used to approximate the local problems at the element level. Numerical results are reported to illustrate the potential of the proposed formulation to efficiently solve Helmholtz problems in homogeneous or heterogeneous media at medium and high frequency regimes.

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