Travel

• September 10-14: NUMDIFF-13 in Halle, Germany
• December 10-14: Reproducibility workshop @ ICERM (Providence)
• December 14-Jan 3: Vacation

Visitors

• OCCAM (Colin Macdonald & Co.): late September
• Janos Pinter (optimization software): October 6-10
• Benson Muite: October 13-15
• Jeff Humpherys (nonlinear wave stability): November 9-15

Papers to be submitted in fall

1. 2D cylindrical stegotons with Manuel (to J. Sci. Comp.)
   • This is complete and ready to be submitted. submitted
2. PeanoClaw (Kristof Unterweger, Tobias Wienzierl, and Aron) (to SISC)
   • debugging
   • Numerical examples
   • Writing
3. Absolute monotonicity of rational functions, with Lajos.
   • Counterexamples to vdG conjecture
   • Proofs of SDIRK and other results
   • Where to submit?
     • Math. of Comp.
     • Advances in Computational Mathematics
     • Foundations of Computational Mathematics
     • J. Sci. Comp.
4. Mix-time integrators (w/Colin Macdonald, Steve Ruuth)
   • Develop interesting examples
   • Writing

Papers to revise after getting referee reports

1. Effective order SSP Runge-Kutta methods, with Yiannis and Colin Macdonald (submitted to SINUM)

2. Optimal RK stability polynomials with Aron (submitted to CAMCOS)

3. Many-stage integrators for spectral difference methods with Matteo and Willem Deconinck (submitted to SISC)

Developing research projects

Direct development:

0. Higher-order downwind Runge-Kutta methods (with Yiannis, Sigal Gottlieb and Sidafa Conde)

• Find families of 3rd and 4th order methods
• Tackle implementation issues?
  • Solvers
  • Boundary conditions

1. Runge-Kutta stability optimization (with Matteo)

• Optimized for SD + Navier-Stokes / high aspect-ratio meshes
• Optimized methods with error estimators
• Combining lower-order time discretizations with higher-order space discretizations

1. General Runge-Kutta optimization (with Matteo)
   • accuracy
   • prescribed dissipation (for multigrid)
2. Comparison of high order extrapolation and deferred correction methods (with Umair bin Waheed)
   • Write up results
   • Practical comparisons
   • Parallel implementation?

Advisory support:

• Computation on the brain with the closest point method:
  • Get Xin’s code working on Shaheen
  • Run Fitzhugh-Nagumo on it when Colin’s group visits

• Convergence of the closest point method (with Colin Macdonal and Tom Maerz)

• SSP explicit multistep Runge-Kutta methods (with Sigal Gottlieb, Zach Grant, Adrian Nemeth)

• Writing and new results from Zach’s code

Ideas

Some ideas that I’m exploring which might become full-fledged projects later in the fall are:

- Internal stability of explicit Runge-Kutta methods with many stages (With Matteo)
- Implicit SSP methods, including multistep multistage, high order downwind, and some good example problems (with Sigal Gottlieb)

Stuff I’m neglecting: - Combinatorial approach to waves in layered media (with Bojan Popov) - Methods for seismic imaging (with Tariq al-Khalifah) - CUDAClaw - Wrap for Python - Work on writing (after George Turkiyyah provides draft)

Week-by-week outline

• Sept. 8-13:
  • DWRK methods
  • Minisymposium at NUMDIFF
• Sept. 15-20:

• High order RK existence

• Sept. 22-26:

• CPM on the brain

• Sept. 29 - Oct. 3:
• Revise PeanoClaw paper
• Diffusion example for mixtime

• Error vector analysis for Hundsdorfer partitioned RK paper

• Oct. 6-10
• Work with Janos Pinter on software for optimizing RK methods

• Revise multistep SSP RK paper

• Oct. 13-17
• Benson Muite visit

• Writing for absolute monotonicity paper

• Oct. 20-24

• RK accuracy optimization

• Oct. 27-31: Eid

• Nov. 3-7

• Nov. 10-14

• Nonlinear wave stability with Jeff Humpherys

• Nov. 17-21

• Nov. 24-28

• Dec. 1-9

• Dec. 10-15: Reproducibility workshop at ICERM