A new development of sixth order accurate compact scheme for the Helmholtz equation (original) (raw)
Access this article
Subscribe and save
- Starting from 10 chapters or articles per month
- Access and download chapters and articles from more than 300k books and 2,500 journals
- Cancel anytime View plans
Buy Now
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Instant access to the full article PDF.
References
- Al-Said, E.A., Noor, M.A., Al-Shejari, A.A.: Numerical solutions for system of second order boundary value problems. Korean J. Comput. Appl. Math. 5(3), 659–667 (1998)
MathSciNet MATH Google Scholar - Ames, W.F.: Numerical Methods for Partial Differential Equations. Academic press, Cambridge (2014)
Google Scholar - Babuška, I.M., Sauter, S.A.: Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM J. Numer. Anal. 34(6), 2392–2423 (1997)
Article MathSciNet MATH Google Scholar - Bayliss, A., Goldstein, C.I., Turkel, E.: The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics. Comput. Math. Appl. 11(7–8), 655–665 (1985)
Article MathSciNet MATH Google Scholar - Bayliss, A., Goldstein, C.I., Turkel, E.: On accuracy conditions for the numerical computation of waves. J. Comput. Phys. 59(3), 396–404 (1985)
Article MathSciNet MATH Google Scholar - Chawla, M.M.: A sixth-order tridiagonal finite difference method for general non-linear two-point boundary value problems. IMA J. Appl. Math. 24(1), 35–42 (1979)
Article MathSciNet MATH Google Scholar - Dastour, H., Liao, W.: A fourth-order optimal finite difference scheme for the Helmholtz equation with PML. Comput. Math. Appl. 78(6), 2147–2165 (2019)
Article MathSciNet Google Scholar - Feng, X., Wu, H.: Discontinuous Galerkin methods for the Helmholtz equation with large wave number. SIAM J. Numer. Anal. 47(4), 2872–2896 (2009)
Article MathSciNet MATH Google Scholar - Fournié, M., Karaa, S.: Iterative methods and high-order difference schemes for 2D elliptic problems with mixed derivative. J. Appl. Math. Comput. 22(3), 349–363 (2006)
Article MathSciNet MATH Google Scholar - Fu, Y.: Compact fourth-order finite difference schemes for Helmholtz equation with high wave numbers. J. Comput. Math. 26, 98–111 (2008)
MathSciNet MATH Google Scholar - Hackbusch, W.: Iterative solution of large sparse systems of equations. Springer, Berlin (1994)
Book MATH Google Scholar - Harari, I., Hughes, T.J.R.: Finite element methods for the Helmholtz equation in an exterior domain: model problems. Comput. Methods Appl. Mech. Eng. 87(1), 59–96 (1991)
Article MathSciNet MATH Google Scholar - Harari, I., Turkel, E.: Accurate finite difference methods for time-harmonic wave propagation. J. Comput. Phys. 119(2), 252–270 (1995)
Article MathSciNet MATH Google Scholar - Ihlenburg, F., Babuška, I.M.: Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM. Comput. Math. Appl. 30(9), 9–37 (1995)
Article MathSciNet MATH Google Scholar - Ihlenburg, F., Babuška, I.M.: Finite element solution of the Helmholtz equation with high wave number part II: the hp version of the FEM. SIAM J. Numer. Anal. 34(1), 315–358 (1997)
Article MathSciNet MATH Google Scholar - Manohar, R.P., Stephenson, J.W.: Single cell high order difference methods for the Helmholtz equation. J. Comput. Phys. 51(3), 444–453 (1983)
Article MATH Google Scholar - Nabavi, M., Siddiqui, M.H.K., Dargahi, J.: A new 9-point sixth-order accurate compact finite-difference method for the Helmholtz equation. J. Sound Vib. 307(3), 972–982 (2007)
Article Google Scholar - Patel, K.S., Mehra, M.: A numerical study of Asian option with high-order compact finite difference scheme. J. Appl. Math. Comput. 57(1–2), 467–491 (2018)
Article MathSciNet MATH Google Scholar - Peiró, J., Sherwin, S.: Finite difference, finite element and finite volume methods for partial differential equations. In: Yip, S. (ed.) Handbook of materials modeling, 2415–2446. Springer (2005)
- Settle, S.O., Douglas, C.C., Kim, I., Sheen, D.: On the derivation of highest-order compact finite difference schemes for the one-and two-dimensional Poisson equation with Dirichlet boundary conditions. SIAM J. Numer. Anal. 51(4), 2470–2490 (2013)
Article MathSciNet MATH Google Scholar - Shaw, R.P.: Integral equation methods in acoustics. Bound. Elem. X 4, 221–244 (1988)
MathSciNet Google Scholar - Sheu, T.W.H., Hsieh, L.W., Chen, C.F.: Development of a three-point sixth-order Helmholtz scheme. J. Comput. Acoust. 16(3), 343–359 (2008)
Article MathSciNet MATH Google Scholar - Singer, I., Turkel, E.: High-order finite difference methods for the Helmholtz equation. Comput. Methods Appl. Mech. Eng. 163(1–4), 343–358 (1998)
Article MathSciNet MATH Google Scholar - Singer, I., Turkel, E.: Sixth-order accurate finite difference schemes for the Helmholtz equation. J. Comput. Acoust. 14(3), 339–351 (2006)
Article MathSciNet MATH Google Scholar - Sutmann, G.: Compact finite difference schemes of sixth order for the Helmholtz equation. J. Comput. Appl. Math. 203(1), 15–31 (2007)
Article MathSciNet MATH Google Scholar - Thomas, J.W.: Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations. Springer, Berlin (2013)
Google Scholar - Turkel, E., Gordon, D., Gordon, R., Tsynkov, S.: Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number. J. Comput. Phys. 232(1), 272–287 (2013)
Article MathSciNet MATH Google Scholar - Wu, T., Xu, R.: An optimal compact sixth-order finite difference scheme for the Helmholtz equation. Comput. Math. Appl. 75, 2520–2537 (2018)
Article MathSciNet MATH Google Scholar - Young, D.M.: Iterative Solution of Large Linear Systems. Elsevier, Amsterdam (2014)
Google Scholar - Zhang, Y., Wang, K., Guo, R.: Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition. Adv. Differ. Equ. 2019(1), 362 (2019)
Article MathSciNet Google Scholar