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

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

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.

Авторлар туралы

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

Әдебиет тізімі

  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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