Comparisons of solving procedures and computation time for Fast Cosine Transformation and Matrix Multiplication Transformation in spectral methods application

References

• D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, Capital City Press, Vermont, 1977.
   Google Scholar
• C. Canuto, and M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, Berlin, 2006.
   Google Scholar
• J. W. Cooley and J. W. Tukey, An Algorithm for Machine Calculation of Complex Fourier Series, Math. Comput., vol. 19, pp. 297–301, 1965.
   Web of Science ®Google Scholar
• J. Shen, T. Tang, and L. L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, Berlin, 2011.
   Google Scholar
• B. Y. Guo, Spectral Methods and Their Applications, World Scientific Publishing Co. Pte. Ltd, Singapore, 1998.
   Google Scholar
• B. W. Li, Y. S. Sun, and Y. Yu, Iterative and Direct Chebyshev Collocation Spectral Method for One-Dimensional Radiative Heat Transfer, Int. J. Heat Mass Transfer, vol. 51, no. 25–26, pp. 5887–5894, 2008.
   Web of Science ®Google Scholar
• B. W. Li, S. Tian, Y. S. Sun, and Z. M. Hu, Schur-decomposition for 3D Matrix Equations and Its Application in Solving Radiative Discrete Ordinates Equations Discretized by Chebyshev Collocation Spectral Method, J. Comput. Phys., vol. 209, pp. 1198–1212, 2010.
   Google Scholar
• S. S. Chen and B. W. Li, Application of Collocation Spectral Domain Decomposition Method to Solve Radiative Heat Transfer in 2D Partitioned Domains, JQSRT, vol. 149, pp. 275–284, 2014.
   Web of Science ®Google Scholar
• P. M. Boomkamp, B. J. Boersma, R. M. Miesen, and G. V. Beijinon, A Chebyshev Collocation Method for Solving Two-Phase Flow Stability Problems, J. Comput. Phys., vol. 132, no. 2, pp. 191–200, 1997.
   Web of Science ®Google Scholar
• B. W. Li, Y. R. Zhao, Y. Yu, and Z. D. Qian, Three-Dimensional Transient Navier–Stokes Solvers in Cylindrical Coordinate System Based on a Spectral Collocation Method Using Explicit Treatment of The Pressure, Int. J. Numer. Methods. Fluids, vol. 66, no. 3, pp. 284–298, 2011.
   Web of Science ®Google Scholar
• Y. Yu, B. W. Li, and A. Thess, The Effect of a Uniform Magnetic Field on Vortex Breakdown in a Cylinder with Rotating Upper Lid, Comput. Fluids, vol. 88, pp. 510–523, 2013.
   Web of Science ®Google Scholar
• X. Y. Leng, Y. Yu, and B. W. Li, Numerical Study of MHD Taylor Vortex Flow with Low Magnetic Reynolds Number in Finite-Length Annulus Under Uniform Magnetic Field, Comput. Fluids, vol. 105, pp. 16–27, 2014.
   Web of Science ®Google Scholar
• H. Wengle and J. H. Seifeld, Pseudospectral Solution of Atmospheric Diffusion Problems, J. Comput. Phys., vol. 26, no. 1, pp. 87–106, 1987.
   Google Scholar
• D. B. Haidvogel, A. R. Robinson, and E. E. Schulman, The Accuracy Efficiency , and Stability of Three Numerical Models with Application to Open Ocean Problems, J. Comput. Phys., vol. 34, no. 1, pp. 1–53, 1980.
   Web of Science ®Google Scholar
• A. Deloff, Semi-Spectral Chebyshev Method in Quantum Mechanics, Ann. Phys., vol. 332, no. 6, pp. 1373–1419, 2007.
   Google Scholar
• R. Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, New York, 2002.
   Google Scholar
• A. K. David, Implementing Spectral Methods for Partial Differential Equations, Springer, Tallahassee, FL, 2009.
   Google Scholar
• A. Karageorghis and T. N. Phillips, Chebyshev Spectral Collocation Methods for Laminar Flow Through a Channel Contraction, J. Comput. Phys., vol. 84, no. 1, pp. 114–133, 1989.
   Web of Science ®Google Scholar
• A. H. Khater, A. B. Shamardan, D. K. Callebaut, and R. S. Ibrahim, Chebyshev Spectral Collocation Methods for Nonlinear Isothermal Magnetostatic Atmospheres, J. Comput. Appl. Math., vol. 115, no. 1–2, pp. 309–329, 2000.
   Web of Science ®Google Scholar
• A. Golbabai and M. Javidi, A Numerical Solution for Non-Classical Parabolic Problem Based on Chebyshev Spectral Collocation Method, Appl. Math. Comput., vol. 190, no. 1, pp. 179–185, 2007.
   Web of Science ®Google Scholar
• A. H. Khater and R. S. Temsah, Numerical Solutions of the Generalized Kuramoto–Sivashinsky Equation by Chebyshev Spectral Collocation Methods, Comput. Math. Appl., vol. 56, no. 6, pp. 1465–1472, 2008.
   Web of Science ®Google Scholar
• F. A. Khasawneh, B. P. Mann, and E. A. Butcher, A Multi-Interval Chebyshev Collocation Approach for the Stability of Periodic Delay Systems with Discontinuities, Commun. Nonlinear. Sci. Numer. Simul., vol. 16, no. 11, pp. 4408–4421, 2011.
   Web of Science ®Google Scholar
• J. Decaix and E. Goncalvès, Compressible Effects Modeling in Turbulent Cavitating Flows, Eur. J. Mech. B., vol. 39, pp. 11–31, 2013.
   Web of Science ®Google Scholar
• R. B. Pelz, The Parallel Fourier Pseudospectral Method, J. Comput. Phys., vol. 92, no. 2, pp. 296–312, 1991.
   Web of Science ®Google Scholar
• P. J. Roache, A Pseudo-Spectral FFT Technique for Non-Periodic problems, J. Comput. Phys., vol. 27, no. 2, pp. 204–220, 1978.
   Web of Science ®Google Scholar
• X. Thibert-Plante, D. A. Yuen, and A. P. Vincent, A Simple Spectral Algorithm for Solving Large-Scale Poisson Equation in 2D, J. Comput. Phys. Comm., vol. 154, no. 2, pp. 89–97, 2003.
   Web of Science ®Google Scholar
• B. Bialecki and A. Karageorghis, Spectral Chebyshev-Fourier Collocation for the Helmholtz and Variable Coefficient Equations in a Disk, J. Comput. Phys., vol. 227, no. 19, pp. 8588–8603, 2008.
   Web of Science ®Google Scholar
• T. D. Taylor, R. S. Hirsh, and M. M. Nadworny, Comparison of FFT, Direct Inversion, and Conjugate Gradient Methods for Use in Pseudo-Spectral Methods, Comput. Fluids, vol. 12, no. 1, pp. 1–9, 1984.
   Web of Science ®Google Scholar
• Y. S. Sun, J. Ma, and B. W. Li, Spectral Collocation Method for Convective–Radiative Transfer of a Moving Rod with Variable Thermal Conductivity, Int. J. Therm. Sci., vol. 90, pp. 187–196, 2015.
   Web of Science ®Google Scholar
• Y. S. Sun, J. Ma and B. W. L, Application of Collocation Spectral Method for Irregular Convective-Radiative Fins with Temperature Dependent Internal Heat Generation and Thermal Properties, Int. J. Thermophys., vol. 36, pp. 3133–3152, 2015.
   Web of Science ®Google Scholar
• J. S. Hesthaven and E. M. Ronquist, Spectral and High Order Methods for Partial Differential Equations, Springer, Heidelberg, 2010.
   Google Scholar
• H. Johnston and J. G. Liu Accurate, Stable and Efficient Navier–Stokes Solvers Based on Explicit Treatment of the Pressure Term, J. Comput. Phys., vol. 199, no. 1, pp. 221–259, 2004.
   Web of Science ®Google Scholar