Galerkin Gradient Least Square Method for Sound Holography in Royaumont Abbey

The Galerkin Gradient Least Square method is here proposed to simulate the sound holography inside the church of the Royaumont abbey, which has been destroyed in 1792. The church is restored with a computer aided design model, which is then meshed by a voxelization algorithm for a finite element analysis. Helmholtz equation is used for modeling the acoustics phenomena. To increase the accuracy of the finite element analysis, a stabilization parameter for the Galerkin Gradient Least Square method is first reviewed in 1D and then devised for 2D and 3D Helmholtz equation. Numerical experiments are carried out to investigate the efficiency of this new stabilization parameter and demonstrate that the Galerkin Gradient Least Square method performs superior to the Galerkin method.