Application of modified integration rule to time-domain finite-element acoustic simulation of rooms.

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.

[1]  Joe LoVetri,et al.  Modeling of the seat dip effect using the finite‐difference time‐domain method , 1996 .

[2]  Manfred Kaltenbacher,et al.  Different Types of Finite Elements , 2008 .

[3]  Albert London,et al.  The Determination of Reverberant Sound Absorption Coefficients from Acoustic Impedance Measurements , 1950 .

[4]  M. Guddati,et al.  Dispersion-reducing finite elements for transient acoustics , 2005 .

[5]  Shinichi Sakamoto,et al.  Phase-error analysis of high-order finite difference time domain scheme and its influence on calculation results of impulse response in closed sound field , 2007 .

[6]  Hideki Tachibana,et al.  Calculation of impulse responses and acoustic parameters in a hall by the finite-difference time-domain method , 2008 .

[7]  D. Botteldooren.  Finite‐difference time‐domain simulation of low‐frequency room acoustic problems , 1995 .

[8]  S. Krenk.  Dispersion-corrected explicit integration of the wave equation , 2001 .

[9]  O. C. Zienkiewicz.  A new look at the newmark, houbolt and other time stepping formulas. A weighted residual approach , 1977 .

[10]  A. Craggs,et al.  A Finite Element Method for the Free Vibration of Air in Ducts and Rooms with Absorbing Walls , 1994 .

[11]  A. Craggs,et al.  Transient response of lightly damped rooms: A finite element approach , 1996 .

[12]  Y. Yasuda,et al.  NUMERICAL ANALYSIS OF LARGE-SCALE SOUND FIELDS USING ITERATIVE METHODS PART I: APPLICATION OF KRYLOV SUBSPACE METHODS TO BOUNDARY ELEMENT ANALYSIS∗ , 2008 .

[13]  Toru Otsuru,et al.  Fundamental accuracy of time domain finite element method for sound-field analysis of rooms , 2010 .

[14]  Toru Otsuru,et al.  Basic characteristics and accuracy of acoustic element using spline function in finite element sound field analysis. , 2000 .