Parallel Spectral Numerical Methods/Acknowledgments

Acknowledgements

The example programs have used a similar structure to those in Trefethen, to which the reader is referred to for further code examples. The codes for the nonlinear Schr?odinger equation were developed in collaboration with Christian Klein and Kristelle Roidot. The codes for the Navier-Stokes equation were developed in collaboration with Hans Johnston. We thank Peter Miller, Brock Palen, David O'Neal, Divakar Viswanath and Jared Whitehead for helpful comments, discussions and suggestions. A class project by Sou-Chi Chang and Sophie Zhang, influenced the presentation of the nonlinear Schr?odinger equation and the exercises on the Gross-Pitaevskii equation, while a class project by Fuzhou Hu and Yutao Qin influenced the presentation and exercises for the two dimensional Navier-Stokes equations. We also thank Daniel Brahan, Emily Cizmas, Kohei Harada, Seth Jordan, Joshua Kirschenheiter, Brian Leu, Albert Liu, Thomas Olsen, Henry Rensch, Parth Sheth, Jeffrey Smolik and Matthew Warnez for constructive criticism and testing the materials. We thank Danny Ellis for providing his notes taken during a lecture on some of this material.

This tutorial was produced using resources of:

• Hopper at the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No.DE-AC02-05CH11231.

• The Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.

• Jaguar at the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

• SCREMS NSF DMS-1026317

Partial financial support was also provided by:

• A curriculum material development grant from The Blue Waters Undergraduate Petascale Education Program administered by the Shodor foundation.

• A Faculty Grant for Innovations in Teaching with Technology from the division of Literature, Sciences and Arts at the University of Michigan.

We also thank Mark Van Moer for his assistance with instrumenting code for coprocessing visualization and providing documentation, which was made possible through the XSEDE Extended Collaborative Support Service (ECSS) program.

References

Trefethen, L.N. (2000). Spectral Methods in Matlab. SIAM.