The direct interpolation boundary element method for solving acoustic wave problems in the time domain

An accurate and general method for transforming domain integrals composed of non-self-adjoint operators into Boundary integrals is still a challenge to overcome. The Direct Interpolation Boundary Element Method (DIBEM) is one of the most recent proposals to achieve this goal. After successfully solving scalar problems governed by the Poisson, Helmholtz, and Diffusive-Advective equations, this work presents the model and results of the DIBEM procedure for approaching acoustic wave propagation problems in the time domain, considering homogeneous media. This work is the first application of DIBEM in dynamics and given the well-known numerical difficulties of this type of problem, the focus is to demonstrate its robustness and precision; however, it also examines numerical features such as the stability of the discrete model, degree of conditioning and positivity of the inertia matrix, valuable effects of poles in the approximation using radial basis functions, and other features. The time advance scheme used was the Houbolt algorithm, whose fictitious damping eliminates spurious modal contents, producing superior stability. Three scalar wave propagation problems that have available analytical solutions are solved.