(An) Efficient multi-domain acoustic BEM for the design sensitivity analysis of interior sound field

Abstract

Multi-domain (or -zone, or -region) boundary element method (MBEM) is the general form of the BEM, in which the interior cavity is divided into several sub-domains connected by hypothetical interface planes. The whole surface pressures and normal velocities on the real and the imaginary surfaces could be obtained by solving the overall linear equation with the given general boundary conditions: Neumann, Dirichlet and Robin conditions. The field pressures, then, were calculated by using SBIE of the single sub-domain and the surface ariables. Through the numerical example, it was observed that the developed program of MBEM could be used as an accurate numerical method for solving the interior acoustic problem. The computational performance of MBEM strongly depends on the shape of the cavity and the division type that includes the number of sub-domains and the locations and shapes of the imaginary interfaces. Although the locations and shapes of the imaginary interfaces would be determined intuitively, it is preferred that the number of sub-domains should be determined under a certain rule to ensure the enhanced accuracy and efficiency in using MBEM. For this purpose, the optimal numbers of sub-domains minimizing the memory size and computation time for constructing and solving matrix equation are derived analytically for the simple two-dimensional cavity modeled by linear boundary elements. As a demonstration example, a two-dimensional long duct modeled with the linear elements is chosen. It is found that the error caused by dividing sub-domains increases as the number of sub-domains is increased because the number of junctions between the imaginary interfaces and the real surfaces are also increased. As a result, the modification of MBEM model through the present guidelines yields more accurate and efficient computation than using SBEM. The number of sub-domains and the locations and shapes of the imaginary interfaces have been determined case by case for dealin...