Solving Thin-Body Acoustic Problems Over an Impedance Plane with a Fast Multipole Indirect Boundary Element Method

This paper presents a fast multipole indirect boundary element solver for the thin-body acoustic problems over an infinite impedance plane. The half-space impedance Green’s function involving a complex line source to approximate the porous ground effects is employed in the indirect boundary integral equation (IBIE), which makes that both mass-like and spring-like impedance conditions on the infinite plane are explicitly satisfied. A nonsingular IBIE formulation is derived to implement the fast multipole method (FMM) easily. The image relations of multipole moments are used to avoid the computation and translation of multipole/local expansion coefficients in the image domain. To deal with the numerical instability in the local translation of image multipole moments, a half-space tree structure is elaborately constructed for the FMM. The validity of the method is testified by a benchmark example and the potential of the method is investigated by the numerical simulation of noise barriers with different geometrical configurations.