Speed gains of the Lumped Parameter Boundary Element Method for vibroacoustics

Current research trends in the acoustical Boundary Element Method (BEM) include efforts to reduce computational and memory costs in order to apply the acoustical BEM on large DOF problems. These efforts mainly focus on improved computational methods (e.g Fast Multipole Methods) or on special assumptions with limited validity. This paper studies a novel approach, which is complementary to many other approaches and which is based upon mathematical and physical considerations that seem quite broadly applicable. The conventional discretization of the acoustic variables with Shape Functions (SF) is replaced by Lumped Parameters (LP). This is called LPBEM in contrast to SFBEM. A major advantage is that less DOF are needed for the accuracies required for practical applications. It is shown that LPBEM offers significant gains both in assembly speed and in solving speed. After introducing the basics of the proposed method, simulations are used to demonstrate the main features and the potential gains of LPBEM. Then some physical and mathematical considerations are offered as a tentative interpretation of the observations.