Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this ... View more
 A. Bayliss, D. Gottlieb, B. J. Matkowsky, and M. Minkoff. An adaptive pseudo-spectral method for reaction diffusion problems. J. Comput. Phys., 81(2):421-443, April 1989.
 John P. Boyd. The arctan/tan and kepler-burgers mappings for periodic solutions with a shock, front, or internal boundary layer. Journal of Computational Physics, 98(2):181 - 193, 1992.
 John P Boyd. Chebyshev and Fourier spectral methods. Courier Dover Publications, 2001.
 Claudio Canuto, M Yousuff Hussaini, Alfio Quarteroni, and Thomas A Zang. Spectral methods in fluid dynamics. 1988.
 Eyal Fattal, Roi Baer, and Ronnie Kosloff. Phase space approach for optimizing grid representations: The mapped fourier method. Phys. Rev. E, 53:1217-1227, Jan 1996.
 S. Futatani, G. Huijsmans, A. Loarte, L.R. Baylor, N. Commaux, T.C. Jernigan, M.E. Fenstermacher, C. Lasnier, T.H. Osborne, and B. Pegourié. Non-linear MHD modelling of ELM triggering by pellet injection in DIII-D and implications for ITER. Nuclear Fusion, 54(7):073008, 2014.
 Hervé Guillard and Roger Peyret. On the use of spectral methods for stiff problems. Computer Methods in Applied Mechanics and Engineering, 66(1):17-43, 1988.
 PB Parks and Re J Turnbull. Effect of transonic flow in the ablation cloud on the lifetime of a solid hydrogen pellet in a plasma. Physics of Fluids (1958-1988), 21(10):1735-1741, 1978.
 R Samtaney, SC Jardin, Phillip Colella, and Daniel F Martin. 3d adaptive mesh refinement simulations of pellet injection in tokamaks. Computer physics communications, 164(1):220- 228, 2004.
 Jie Shen and Li-Lian Wang. Error analysis for mapped legendre spectral and pseudospectral methods. SIAM J. Numer. Anal, 42:326-349, 2004.