MPO672 Course Material

References

Spectral And Spectral Element Methods

• Lloyd Nicholas Trefethen, Spectral methods in MATLAB, SIAM, Philadelphia Pa, 2000.
• John P. Boyd, Chebyshev and Fourier Spectral Methods Dover Publications, 2000. (Spectral methods)
• Bengt Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, Cambridge, 1998.
• C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods-Fundamental in Single Domains, Springer-Verlag, New York, 2006.
• Martin Ehrendorfer, Spectral Numerical Weather Prediction Models, ISBN13: 9781611971989, SIAM, PA, 2011.
• C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods-Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer-Verlag, New York, 2007.
• George Em. Karniadakis and Spencer J. Sherwin, Spectral $h-p$ Element Methods for CFD, New York, Oxford University Press, 1999.
• Michel O. Deville and Paul F. Fischer and E.H. Mund High-Order Methods for Incompressible Fluid Flow, Cambridge University Press, 2002.
• David A. Kopriva Implementing Spectral Methods for Partial Differential Equations Algorithms for Scientists and Engineers Springer-Verlag, 2009.
• Roger Peyret Spectral methods for incompressible viscous flow Springer-Verlag, 2002.
• Jan S. Hesthaven, Sigal Gottlieb, David Gottlieb Spectral methods for time-dependent problems Cambridge University Press, 2007.
• David Gottlieb, Steven A. Orszag Numerical analysis of spectral methods: theory and applications SIAM, Philadelphia Pa, 1993.

Finite Element Methods

• Howard C. Elman, David J. Silvester, Andrew J. Wathen Finite elements and fast iterative solvers with applications in incompressible fluid dynamics , Oxford University Press, Oxford ; New York , 2005.
• Philip M. Gresho, and Robert L. Sani, and M.S. Engelman}, Incompressible Flow and the Finite Element Method : Advection-diffusion and Isothermal Laminar Flow, John Wiley \& Sons, Ltd. (UK), 1999.
• O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu Finite Element Method - Its Basis and Fundamentals (6th Edition) 2005 Elsevier
• O.C. Zienkiewicz, R.L. Taylor, and P. Nithiarasu, Finite Element Method for Fluid Dynamics (6th Edition) 2005 Elsevier
• Gilbert Strang and George J. Fix, An analysis of the finite element method Englewood Cliffs, N.J., Prentice-Hall ,1973

Notes

• Polynomial Spectral Expansion
• Gaussian Quadrature
• Solution of PDE using Collocation. The directory Collocation contains matlab scripts for numerical experimentation.
• Solution of PDE using Spectral Projection. The directory Spectral contains matlab scripts for numerical experimentation.
• Solution of PDE using Spectral Projection. The directory WeakForm contains matlab scripts for numerical experimentation.

Final Projects

• Simulation of tsunami propagation in Galapagos using spectral element shallow water model.
• Simulation of gravity currents with 2D spectral element NS solving written using a vorticity-streamfunction formulation

Tutorials and Manuals

• Skeleton script for symbolic manipulation in matlab.

Spectral Element Model