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Development of 3D PUFEM with linear tetrahedral elements for the simulation of acoustic waves in enclosed cavities

机译:具有线性四面体元素的3D PUFEM的开发,用于模拟封闭腔中的声波

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This work is concerned with the numerical simulation of sound pressure field in three-dimensional cavities in which absorbing materials are present. Standard techniques such as the Finite Element Method are known to be extremely demanding computationally when the frequency increases and thus limited to low frequency applications. To alleviate these difficulties, an alternative formulation based on the Partition of Unity Finite Element Method is proposed. The method involves enriching the approximation finite element space by expanding the acoustic pressure in a set of plane waves propagating in various directions over the unit sphere. Particular attention is devoted to the fast and accurate computation of highly oscillatory integrals which is required by the method. Convergence studies show that these wave finite elements allow to capture accurately the wave field with a number of degrees of freedom that only grows quadratically with the frequency yielding drastic data reduction compared to classical FEM. Results of practical interest are shown for the case of a sound source placed in a reverberation room with absorbing materials. (C) 2018 Elsevier B.V. All rights reserved.
机译:这项工作与存在吸收材料的三维腔体中声压场的数值模拟有关。众所周知,当频率增加时,诸如有限元法之类的标准技术对计算的要求非常高,因此仅限于低频应用。为了缓解这些困难,提出了一种基于统一有限元方法的替代公式。该方法包括通过扩大在单位球面上向各个方向传播的一组平面波中的声压来丰富近似有限元空间。该方法要求特别注意快速且准确地计算高度振荡积分。收敛性研究表明,与经典FEM相比,这些波有限元可以精确捕获具有多个自由度的波场,这些自由度仅随着频率的平方增长而产生急剧的数据降低。对于将声源放置在带有吸收材料的混响室中的情况,显示了具有实际意义的结果。 (C)2018 Elsevier B.V.保留所有权利。

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