Acoustic calculations with the hybrid boundary element method in time domain

The boundary element method (BEM) is an efficient tool for the calculation of acoustic wave propagation in fluids. Transient waves can be solved by ei ther using a formulation in frequency domain along with an inverse Fourier transformation or a time domain formulation. To increase the efficiency for the solver and allow for an efficient coupling with finite element domains the symmetry of the system matrices is advantageous. If Hamilton's princip le is used, a symmetric variational formulation can be established with the velocity potential as field variable. The single field principle is genera lized as multifield principle as basis of a hybrid BEM for the calculation of acoustic fields in compressible fluids in time domain. The state variabl es are separated into boundary variables, which are approximated by piecewi se polynomials and domain variables, which are approximated by a superposit ion of weighted fundamental solutions. In both approximations the time and space dependency is separated. This is why static fundamental solution can be used for the field approximation. The domain integrals are eliminated, r espectively, transformed into boundary integrals and an equation of motion with symmetric mass and stiffness matrix is obtained, which can be solved b y a direct time integration scheme or by mode superposition. The time deriv ative of the equation of motion leads to a formulation with pressure and ac oustic flux on the boundary for an easier interpretation of the variables. (C) 2001 Elsevier Science Ltd. All rights reserved.