yiannis/fall_2013
Fall 2013 research plans
Primary goals
- Efficient solution of nonlinear system for downwind implicit RK methods.
- Finilize work on strong stability preservation of additive multistep methods (theoretical and numerical results).
- Work on boundary conditions of RK and multistep methods with downwinding.
Week-by-week schedule
September 8 - 12:
- Prove result about SSP region of additive multistep methods with downwinding.
- Edit and complete matlab code for solving PDEs/ODEs using downwind methods.
September 15 - 19:
- Prove remaining results for monotonicity of downwind ALMM (SSP coefficient bound for downwind ALMM of order more than one)
- Investigate if different FE assumptions for additive methods give larger allowed time-steps for monotonicity.
- Find analytical Jacobian for 1st and 2nd order TVD discretizations.
September 22 - 26:
- Find analytical Jacobian for 1st and 2nd order TVD discretizations (cont.)
- Write python code for solving hyperbolic PDEs/ODEs using downwind methods
- Wrap-up results for downwind multistep methods.
September 29 - October 3:
- Write python code for solving hyperbolic PDEs/ODEs using downwind methods (cont.)
October 6 - 10:
- Search for possible implicit DWSSPRK(s,3), s>3 and DWSSPRK(s,4) with arbitrary large SSP coefficient.
- Study Jacobian-free approaches to solve implicit problems:
- Read Jacobian-free Newton–Krylov methods: a survey of approaches and applications (D.A. Knoll, D.E. Keyes) and relevant papers.
October 13 - 17:
- Eid Al Adha
October 20 - 24:
- Study Jacobian-free approaches to solve implicit problems (cont.)
