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<p>In this paper we investigate a stable space–time formulation for long-time industrial sound emission problems. To this end, we use a well-posed Galerkin formulation in space and time of the acoustic wave equation in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>, involving a hypersingular boundary integral operator. Our numerical experiments confirm that the resulting time stepping scheme is stable and accurate for complex acoustic problems in industrial geometries, in contrast to alternative well-known schemes. The proposed method is shown to be efficient for real-world problems, and we obtain very good agreement with physical acoustic measurements.</p>

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A stable boundary element method for reliable long-time industrial sound emission

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月18日

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  • Simon Schneider,
  • Ceyhun Özdemir,
  • Heiko Gimperlein,
  • Karsten Urban,
  • Bernd Graf

摘要

In this paper we investigate a stable space–time formulation for long-time industrial sound emission problems. To this end, we use a well-posed Galerkin formulation in space and time of the acoustic wave equation in \(\mathbb {R}^3\) R 3 , involving a hypersingular boundary integral operator. Our numerical experiments confirm that the resulting time stepping scheme is stable and accurate for complex acoustic problems in industrial geometries, in contrast to alternative well-known schemes. The proposed method is shown to be efficient for real-world problems, and we obtain very good agreement with physical acoustic measurements.