Efficiency of room acoustic simulations with time-domain FEM including frequency-dependent absorbing boundary conditions: Comparison with frequency-domain FEM

A Parallel Dissipation-Free and Dispersion-Optimized Explicit Time-Domain FEM for Large-Scale Room Acoustics Simulation

“…Taking the Galerkin method with three BCs in Equation (2) leads to the second-order ordinary differential equation (ODE) as [45]…”

“…As shown in numerical simulations conducted in Section 3, the Crank-Nicolson method has good accuracy and stability in the time-marching calculations for the accumulators. Details of the Crank-Nicolson method implementation are presented in an earlier report of the literature [45]. With the help of ADE method, Equation ( 4) is transformed into…”

“…The comparison was made using a mean sound pressure level (SPL) among six receivers at frequencies of 100 Hz to 1.2 kHz. Here, the SPL is a transfer function removing sound source characteristics in time-domain results according to a procedure described in an earlier report [45]. As a quantitative measure, the similarity of frequency responses between the FD-FEM result and the TD-FEM result were evaluated using the cross-correlate coefficient with respect to mean SPL CC L m as…”

“…The present section presents a discussion of performances of the 4th-E TD-FEM and the Opt-E TD-FEM compared to the two existing implicit TD-FEMs [27,45], i.e., the fourth-order accurate implicit TD-FEM (4th-I) and the standard second-order implicit TD-FEM (2nd-I) in broadband room acoustic modeling. For Opt-E TD-FEM, we use the four optimized settings shown in Section 2.4.…”

“…A local-reaction BC that simplifies the incident-angle dependence is another selection because the computation becomes easier with the surface impedance of sound absorbers than the extended-reaction BCs that require discretization of materials according to corresponding partial differential equations. Although the implementation of frequency-dependence into time-domain methods is difficult because of the inclusion of convolution operation, very recently developed time-domain methods [23,[41][42][43][44][45] can specifically address the frequency-dependence in the local-reaction BC and extended-reaction BC efficiently. This report also addresses the implementation of frequency-dependent local-reaction impedance BCs into the dissipation-free and dispersion-optimized explicit TD-FEM using auxiliary differential equations method [46].…”