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The applicability of the modified integration rule for time-domain finite-element analysis is tested in sound field analysis of rooms involving rectangular elements, distorted elements, and finite impedance boundary conditions. Dispersion error analysis in three dimensions is conducted to evaluate the dispersion error in time-domain finite-element analysis using eight-node hexahedral elements. The results of analysis confirmed that fourth-order accuracy with respect to dispersion error is obtainable using the Fox-Goodwin method (FG) with a modified integration rule, even for rectangular elements. The stability condition in three-dimensional analysis using the modified integration rule is also presented. Numerical experiments demonstrate that FG with a modified integration rule performs much better than FG with the conventional integration rule for problems with rectangular elements, distorted elements, and with finite impedance boundary conditions. Further, as another advantage, numerical results revealed that the use of modified integration rule engenders faster convergence of the iterative solver than a conventional rule for problems with the same degrees of freedom.

This paper presents a finite element method (FEM) using hexahedral 27node spline acoustic elements (Spl27) with low numerical dispersion for room acoustics simulation in both the frequency and time domains, especially at higher frequencies. Dispersion error analysis in one dimension is performed to increase the accuracy of FEM using Spl27 by modifying the numerical integration points of element stiffness and mass matrices. The basic accuracy and efficiency of the FEM using the improved Spl27, which uses modified integration points, are presented through numerical experiments using benchmark problems in both the frequency and time domains, revealing that FEM using the improved Spl27 in both domains provides more accurate results than the conventional method does, and with fewer degrees of freedom. Moreover, the effectiveness of FEM using the improved Spl27 over that using hexahedral 27-node Lagrange elements is shown for time domain analysis of the sound field in a practical sized room.

An in-situ measurement technique of a material surface normal impedance is proposed. It includes a concept of "ensemble averaged" surface normal impedance that extends the usage of obtained values to various applications such as architectural acoustics and computational simulations, especially those based on the wave theory. The measurement technique itself is a refinement of a method using a two-microphone technique and environmental anonymous noise, or diffused ambient noise, as proposed by Takahashi et al. [Appl. Acoust. 66, 845-865 (2005)]. Measured impedance can be regarded as time-space averaged normal impedance at the material surface. As a preliminary study using numerical simulations based on the boundary element method, normal incidence and random incidence measurements are compared numerically: results clarify that ensemble averaging is an effective mode of measuring sound absorption characteristics of materials with practical sizes in the lower frequency range of 100-1000 Hz, as confirmed by practical measurements.

This paper presents an assessment of the accuracy and applicability of a time domain finite element method (TDFEM) for sound-field analysis in architectural space. This TDFEM incorporates several techniques: (1) a hexahedral 27-node isoparametric acoustic element using a spline function; (2) a lumped acoustic dissipation matrix; and (3) Newmark time integration method with an absolute diagonal scaled COCG iterative solver. Sound fields in an irregularly shaped reverberation room of 166 m 3 are computed using TDFEM. The computed values and measured values for 125-500 Hz are compared, revealing that the fine structure of the computed band-limited impulse responses agree with measured ones up to 0.1 s, with a cross correlation coefficient greater than 0.93. The cross correlation coefficient decreases gradually over time, and more rapidly for higher frequencies. Moreover, the computed decay curves, and the reverberation times, agree well with the respective measured ones, and with a better fit the higher the frequency (up to 500 Hz).

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Krylov subspace iterative solvers are applied to large-scale finite element sound-field analyses of architectural rooms. First, convergence behaviors are compared among four iterative solvers. Results show that the Conjugate Orthogonal Conjugate Gradient (COCG) method offers the best characteristics for finite-element (FE) analysis from the viewpoint of robustness of convergence and computation time. Two investigations to reduce the computation time of the COCG method were carried out. Results show the following. (1) The mean residual of sound pressure levels between COCG method and direct method is less than 0.1 dB if the convergence criterion is set to 10-4 and the maximum residual of those between COCG method and direct method is less than 0.2 dB if the convergence criterion is set to 10-6. (2) The computation time of the COCG method with diagonal preconditioning is about 30% shorter than that of COCG method without preconditioning. Finally, sound pressure level distributions obtained using the authors' FEM are compared to those obtained using fast multipole BEM (FMBEM) and measurements.

The convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3D acoustical BEM is investigated through numerical experiments. The fast multipole BEM, which is an efficient BEM based on the fast multipole method, is used for solving problems with up to about 100,000 DOF. It is verified that the convergence behavior of solvers is much affected by the formulation of the BEM (singular, hypersingular, and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCGStab2 have more stable convergence than others, and these solvers are useful when solving interior problems in basic singular formulation. When solving exterior problems with greatly complex shape in Burton-Miller formulation, all solvers hardly converge without preconditioning, whereas the convergence behavior is much improved with ILU-type preconditioning. In these cases GMRes is the fastest, whereas CGS is one of the good choices, when taken into account the difficulty of determining the timing of restart for GMRes. As for calculation for rigid thin objects in hypersingular formulation, much more rapid convergence is observed than ordinary interior/exterior problems, especially using BiCG-like solvers.