Travel

• Feb. 20-28 SIAM CSE meeting (Boston)

Visitors

• Feb. 2-14 Zoltan
• Feb. 2-7 Adrian and Tihi

Arrivals

• March 9: Benson Muite

Papers to be submitted in spring

1. PeanoClaw (Kristof Unterweger, Tobias Wienzierl, and Aron) Submitted to SISC.

2. Absolute monotonicity of rational functions, with Lajos.
   • Counterexamples to vdG conjecture
   • Proofs of SDIRK and other results
   • For submission to LMS JCM.
3. Internal error propagation (with Lajos, Matteo, and Yiannis)
   • Develop interesting examples
   • Proofs
   • Writing
4. Comparison of high order extrapolation and deferred correction methods (with Umair bin Waheed)
   • Write up results
   • Practical comparisons
   • Parallel implementation?

Papers to revise after getting referee reports

1. 2D cylindrical stegotons with Manuel (submitted to J. Sci. Comp.)
   • Resubmitted

2. Spatially partitioned embedded RK methods (submitted to SINUM)

3. Effective order SSPRK
   • Resubmitted?

Developing research projects

1. 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

2. Optimal splittings of Runge-Kutta methods (with Higueras, Adrian)

3. Many-stage RK methods for Navier-Stokes (with Matteo)
   • Write section on RK stability
4. SSP explicit multistep Runge-Kutta methods (with Sigal Gottlieb, Zach Grant, Adrian Nemeth)
   • Writing and new results from Zach’s code

5. Variable step-size SSP linear multistep methods (with Adrian, Lajos)

6. Accuracy optimization of Runge-Kutta methods for PDEs

Ideas

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

Week-by-week outline

• Jan. 26-30:
  • PeanoClaw convergence tests
  • Prepare teaching materials for AMCS 252
  • Review proofs in absolute monotonicity paper
  • Writing for extrapolation paper
• Feb. 2-13:
  • Work with Zoltan, Adrian, and Tihi on positivity and SSP
• Feb. 16-19:
  • Prepare presentations
  • Finish PeanoClaw, absolute monotonicity, and/or extrapolation papers

• Feb. 20-28: Travel to USA, attend SIAM CSE ’13

• March 2-6:
  • Revise absolute monotonicity paper
  • Write parallel extrapolation code
  • Add PDE examples to extrapolation paper
• March 9-13:
  • Organize SSP LMM bounds paper
  • Organize and flesh out optimal splittings paper

• March - May: TBD