A computational acoustic field reconstruction process based on an indirect boundary element formulation

The objective of the work presented in this paper is to develop a computational capability based on the indirect boundary element method (IBEM) for evaluating appropriate velocity boundary conditions on an assembly of piston type sources in order to recreate a prescribed acoustic field. Information for the acoustic pressure of the original acoustic field at certain field points constitutes the input to the developed process. The velocities on the piston type sources are computed from transfer functions evaluated between the field points where the acoustic pressure of the original field is prescribed and the velocity boundary condition on each element of the generic source. The IBEM is employed for computing the transfer functions in order to accommodate the presence of openings in the model and radiation from both sides of the piston type sources. Simulating the generic source as a thin surface that radiates from both sides eliminates the presence of irregular frequencies in the analysis. A singular value decomposition (SVD) solver is integrated with the IBEM computations in order to evaluate the velocity boundary conditions from the transfer functions. The number of field points where the acoustic pressure is defined can be considerably smaller than the number of elements where the velocity is computed. The solution that demonstrates the smallest magnitude is selected from all possible solutions. An algorithm is also developed for identifying the optimum field points where the acoustic pressure of the original field must be prescribed. The optimum field points are selected from a set of prescribed candidate points. The number of optimum points is considered smaller than the number of elements where the velocity is computed. The properties of the transformation matrix and the quality of the reconstruction depend on the location of the field points. Thus, the selection of the optimum points is based on achieving the highest possible orthogonality among the vectors that comprise the range of the transformation matrix. Several validation and application cases are presented.