Time-harmonic Acoustics
In addition to electromagnetics our research group has also carried out a considerable amount of research on linearized time-harmonic acoustics. We have investigated and developed Galerkin's type discretization schemes for acoustics surface integral equation methods. This approach effectively avoids the previously reported problems associated with the point-collocation discretization of the hyper-singular boundary integral operator arising from the Burton-Miller integral equation formulation. We have also studied the use of higher order polynomial basis functions to model the surface pressure and developed accurate numerical methods based on the singularity subtraction technique for evaluating integrals in singular and near-singular cases.
In order to consider problems with a high number of unknowns, we have investigated iterative solution of a dense linear system arising from the Galerkin discretization of the Burton-Miller formulation with the GMRES method. To expedite the convergence of the GMRES method incomplete LU (ILU) preconditioner is applied. The developed formulation was found to lead to rapidly converging iterative solutions and hence, can be coupled with a fast solver, the multilevel fast multipole algorithm (MLFMA). In particular, we have developed a broadband version of MLFMA that can be used on a very wide frequency range from nearly zero frequency up to tens kHz.
- Galerkin discretization for the Burton-Miller integral equation.
- High-order basis functions and singularity extraction technique.
- GMRES, ILU preconditioner and MLFMA for solving large problems.
References
- H. Wallen, S. Järvenpää and P. Ylä-Oijala: Broadband multilevel fast multipole algorithm for acoustic scattering problems, Journal of Computational Acoustics, 14(4), 507 - 526, 2006.
- P. Ylä-Oijala and S. Järvenpää: Iterative solution of high-order boundary element method for acoustic impedance boundary value problems, Journal of Sound and Vibration, 291, 824-843, 2006.
- S. Järvenpää, M. Taskinen and P. Ylä-Oijala: Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra, International Journal for Numerical Methods in Engineering, vol. 58, pp. 1149-1165, 2003.