TRANSPARENT BOUNDARY CONDITIONS FOR THE WAVE EQUATION WITH VARIABLE SPEED OF SOUND

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详细

A method of constructing a transparent boundary condition operator for a wave equation with variable sound velocity in a channel of rectangular cross section is proposed. A numerical example showing the performance of the proposed method is given. Properties of images of the convolution kernel functions of transparent boundary conditions are analyzed, a method of constructing their rational approximation is proposed, and its numerical convergence is shown.

作者简介

A. Aptekarev

M.V. Keldysh Institute of Applied Mathematics; Lomonosov Moscow State University

Email: aptekaa@keldysh.ru
Moscow, Russia; Moscow, Russia

N. Zaitsev

M.V. Keldysh Institute of Applied Mathematics; Lomonosov Moscow State University

Email: nikolai_zaitsev@mail.ru
Moscow, Russia; Moscow, Russia

参考

  1. Givoli D. Nonreflecting boundary conditions // J. Comp. Phys. 1991. V. 94. P. 1–29.
  2. Lyriutzis A.S. Review: The Use of Kirchhoff's method in computational aeroacoustics // J. of Fluids Engng. 1994. V. 116. № 12. Р. 665–676.
  3. Tsynkov S.V. Numerical solution of problems on unbounded domains. A review // Appl. Numer. Math. 1998. V. 27. Р. 465–532.
  4. Hagstrom T. New results on absorbing layers and radiation boundary conditions // Topics in Computational Wave Propagation, M. Ainsworth, P. Davies, D. Duncan, P. Martin, and B. Rynne, eds., Springer-Verlag. 2003. P. 1–42.
  5. Givoli D. High-Order Local Non-Reflecting Boundary Conditions: A Review // Wave Motion. 2004. V. 39. Р. 319–326.
  6. Codponoa H.JI. Условия полной прозрачности на сфере для трехмерного волнового уравнения // Докл. АН. 1992. Т. 326. № 6. С. 453–457.
  7. Codponoa H.JI. Условия полной прозрачности для волнового уравнения // Препринт ИПМ им. М. В. Келдыша. 1993. № 76.
  8. Grote M., Keller J. Exact nonreflecting boundary conditions for the time dependent wave equation // SIAM J. Appl. Math. 1995. V. 55. № 2.
  9. Sofronov I.L. Artificial boundary conditions of absolute transparency for two- and three-dimensional external time-dependent scattering problems // Euro. J. Appl. Math. 1998. V. 9. № 6. Р. 561–588.
  10. Hagstrom T. Radiation boundary conditions for the numerical simulation of waves // Acta Numer. 1999. V. 8. Р. 47–106.
  11. Alpert B., Greengard L., Hagstrom T. Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation // J. of Computational Physics. 2002. V. 180. Р. 270–296.
  12. Zaitsev N.A. Transparent Boundary Conditions for the Wave Equation in a Channel of Circular Section // Lobachevskii Journal of Mathematics. 2021. V. 42. № 11. Р. 2675–2683.
  13. Petrov P.S., Elnhardt M. Transparent boundary conditions for iterative high-order parabolic equations // J. of Computational Physics. 2016. V. 313. Issue C. Р. 144–158.
  14. Lytaev M.S. An Improved Accuracy Split-Step Padii Parabolic Equation for Tropospheric Radio-Wave Propagation // In: Gervasi O., et al. Computational Science and Its Applications – ICCSA 2021. Lecture Notes in Computer Science. V. 12949. Р. 418–433.
  15. Codponoa H.JI., Довешович Л.Е., Krasnov Н.А. Об аппроксимации прозрачных граничных условий с высоким порядком точности для волнового уравнения // Компьютерные исследования и моделирование. 2014. V. 1. Р. 45–56.
  16. Alpert B., Greengard L., Hagstrom T. Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation // SIAM J. Num. Anal. 2000. V. 37. Р. 1138.
  17. Антекарев А.Н., Боголюбский А.Н., Япицелев М.Л. Сходимость лучевых последовательностей аппроксимаций Фробениуса–Паде // Матем. сб. 2017. Т. 208. № 3. С. 4–27.
  18. Зайцев Н.А., Винниченко А.А. Прозрачные граничные условия для численного моделирования волновых процессов в квадратной области // Матем. моделирование. 2011. Т. 23. № 11. С. 5–20.

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