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Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1404). A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions. سامانه مدیریت نشریات علمی, 13(4), 1385-1399. doi: 10.22034/cmde.2024.60344.2577
Santosh Kumar Bhal; Ashish Kumar Nandi; Abedallah Rababah. "A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions". سامانه مدیریت نشریات علمی, 13, 4, 1404, 1385-1399. doi: 10.22034/cmde.2024.60344.2577
Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. (1404). 'A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions', سامانه مدیریت نشریات علمی, 13(4), pp. 1385-1399. doi: 10.22034/cmde.2024.60344.2577
Bhal, Santosh, Nandi, Ashish, Rababah, Abedallah. A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions. سامانه مدیریت نشریات علمی, 1404; 13(4): 1385-1399. doi: 10.22034/cmde.2024.60344.2577

A higher-order orthogonal collocation technique for discontinuous two-dimensional problems with Neumann boundary conditions

Computational Methods for Differential Equations
مقاله 22، دوره 13، شماره 4، دی 2025، صفحه 1385-1399    اصل مقاله (449.81 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60344.2577
نویسندگان
Santosh Kumar Bhal1؛ Ashish Kumar Nandi* 2؛ Abedallah Rababah3
1Department of Mathematics, School of Advanced Sciences and Languages, Vellore Institute of Technology, Bhopal, India.
2Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu-600127, India.
3Department of Mathematical Sciences, United Arab Emirates University, United Arab Emirates.
چکیده
In this paper, the orthogonal spline collocation method (OSCM) is employed to address the solution of the Helmholtz equation in two-dimensional problems. It is characterized by discontinuous coefficients with certain wave numbers. The solution is approximated by employing distinct basis functions, namely, monomial along the x-direction and Hermite along the y-direction. Additionally, to solve the two-dimensional problems efficiently in the sense of computational cost with fewer operation counts, the matrix decomposition algorithm (MDA) is used to convert them into a set of one-dimensional problems. As a consequence, the resulting reduced matrix becomes non-singular in discrete cases. To assess the performance of the proposed numerical scheme, a grid refinement analysis is conducted to incorporate various wave coefficients of the Helmholtz equation. The illustrations and examples demonstrate a higher order of convergence compared to existing methods.
کلیدواژه‌ها
Helmholtz equation؛ Orthogonal spline collocation methods؛ Matrix decomposition algorithm
مراجع
  • [1] A. Aghili and A. H. Shabani, Application of the orthogonal collocation method in evaluating the rate of reactions using thermogravimetric analysis data Thermochimica Acta, (2024), 179698.
  • [2] S. K. Bhal and P. Danumjaya, A Fourth-order orthogonal spline collocation solution to 1D-Helmholtz equation with discontinuity, The Journal of Analysis, 27 (2019), 377–390.
  • [3] S. K. Bhal, P. Danumjaya, and G. Fairweather, A fourth–order orthogonal spline collocation method for twodimensional Helmholtz problems with interfaces, Numerical Methods for Partial Differential Equations, 36(6) (2020), 1811–1829.
  • [4] S. K. Bhal, P. Danumjaya, and G. Fairweather, High-order orthogonal spline collocation methods for two-point boundary value problems with interfaces, Mathematics and Computers in Simulation, 174 (2020), 102–122.
  • [5] S. K. Bhal, P. Danumjaya, and A. Kumar, A fourth-order orthogonal spline collocation method to fourth-order boundary value problems, International Journal for Computational Methods in Engineering Science and Mechanics, 20(5) (2019), 460–470.
  • [6] B. Bialecki and G. Fairweather, Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions, Journal of Computational and Applied Mathematics, 46(3) (1993), 369–386.
  • [7] B. Bialecki and G. Fairweather, Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems, SIAM Journal on Scientific Computing, 16(2) (1995), 330–347.
  • [8] B. Bialecki and G. Fairweather, Orthogonal spline collocation methods for partial differential equations, Journal of Computational and Applied Mathematics, 128 (2001), 55–82.
  • [9] B. Bialecki, G. Fairweather, and K. R. Bennett, Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocations equations, SIAM Journal on Numerical Analysis, 29(1) (1992), 156–173.
  • [10] B. Bialecki, G. Fairweather, and A. Karageorghis, Matrix decomposition algorithms for elliptic boundary value problems: a survey, Numerical Algorithms, 56 (2011), 253–295.
  • [11] B. Bialecki, G. Fairweather, and K. A. Remington, Fourier methods for piecewise Hermite bicubic orthogonal spline collocation, East-West Journal of Numerical Mathematics, 2 (1994), 1–20.
  • [12] R. Dautray and J. L. Lions, Mathematical analysis and numerical methods for science and technology, SpringerVerlag, New York, 1990.
  • [13] C. De Boor and B. Swartz, Collocation at Gauss points, SIAM Journal on Numerical Analysis, 10(4) (1973), 582–606.
  • [14] J. C. Diaz, G. Fairweather, and P. Keast, Algorithm 603 COLROW and ARCECO: Packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination, ACM Transactions on Mathematical Software, 9(3) (1983), 376–380.
  • [15] D. S. Dillery, High order orthogonal spline collocation schemes for elliptic and parabolic problems, Thesis (Ph.D.), University of Kentucky, 1994.
  • [16] W. R. Dyksen, Tensor product generalized ADI methods for separable elliptic problems, SIAM Journal on Numerical Analysis, 24(1) (1987), 59–76.
  • [17] G. Fairweather and D. Meade, A survey of spline collocation methods for the numerical solution of differential equations, Mathematics for Large Scale Computing, CRC press, (1989), 297–341.
  • [18] X. Feng, A high-order compact scheme for the one-dimensional Helmholtz equation with a discontinuous coefficient, International Journal of Computer Mathematics, 89(5) (2012), 618–624.
  • [19] L. Feng, F. Geng, and L. Yao, Numerical solutions of Schr¨odinger-Boussinesq system by orthogonal spline collocation method, Journal of Computational and Applied Mathematics, (2024), 115984.
  • [20] X. Feng, Z. Li, and Z. Qiao, High-order compact finite difference schemes for the Helmholtz equations with discontinuous coefficients, Journal of Computational Mathematics, 29 (2011), 324–340.
  • [21] Y. Fu, Compact fourth-order finite difference schemes for Helmholtz equation with high wave numbers, Journal of Computational Mathematics, (2008), 98–111.
  • [22] B. Guy, G. Fibich, and S. Tsynkov, High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension, Journal of Computational Physics, 227(1) (2007), 820–850.
  • [23] B. Guy, G. Fibich, S. Tsynkov, and E. Turkel, Fourth order schemes for time-harmonic wave equations with discontinuous coefficients, Communications in Computational Physics, 5 (2009), 442–455.
  • [24] F. Ihlenburg and I. Babuˇska, Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM, Computers & Mathematics with Applications, 30(9) (1995), 9–37.
  • [25] K. Ito, Z. Qiao, and J. Toivanen, A domain decomposition solver for acoustic scattering by elastic objects in layered media, Journal of Computational Physics, 227(19) (2008), 8658–8698.
  • [26] M. C. Junger and D. Feit, Sound, structures and their interaction, Cambridge, MA: MIT press, 1986.
  • [27] P. M. Prenter and R. D. Russell, Orthogonal collocation for elliptic partial differential equations, SIAM Journal on Numerical Analysis, 13(6) (1976), 923–939.
  • [28] A. Rakhim, Existence and uniqueness for a two-point interface boundary value problem, Electronic Journal of Differential Equations, 242 (2013), 1–12.
  • [29] M. P. Robinson and G. Fairweather, Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems, Journal of Computational Acoustics, 1(3) (1993), 355–370.
  • [30] E. Roubine, Étude des ondes electromagnetiques guidees par les circuits en helice, Annales des Télécommunications, 7 (1952), 206–216.
  • [31] I. H. Sloan, D. Tran, and G. Fairweather, A fourth-order cubic spline method for linear second-order two point boundary value problems, IMA Journal of Numerical Analysis, 13(4) (1993), 591–607.
  • [32] A. Uri, S. Pruess, and R. D. Russell, On spline basis selection for solving differential equations, SIAM Journal on Numerical Analysis, 20(1) (1983), 121–142.
  • [33] R. Wang, Y. Yan, A. S. Hendy, and L. Qiao, BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions, Computers & Mathematics with Applications, 155 (2024), 126–141.
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