Let c_eff be the minimum number of function evaluations required to step as far as one step of forward Euler while still being SSP. Some theoretical bounds
1. There are no explicit methods with c_eff > 1.
2. There are no explicit methods beyond order 4 (for nonlinear problems) and c_eff > 0.
3. There are no implicit methods with order greater than 1 and c_eff > 2.
This integrator provides Runge-Kutta methods of order 2, 3, and 4 with maximal values of c_eff. More stages allows for larger values of c_eff which improves efficiency. These implementations are low-memory and only use 2 or 3 work vectors regardless of the total number of stages, so e.g. 25-stage 3rd order methods may be an excellent choice.
Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104}
rks2: Second order methods with any number s>1 of stages. c_eff = (s-1)/s
rks3: Third order methods with s=n^2 stages, n>1. c_eff = (s-n)/s
rk104: A 10-stage fourth order method. c_eff = 0.6
1. | - Ketcheson, Highly efficient strong stability preserving Runge Kutta methods with low storage implementations, SISC, 2008. | |
2. | - Gottlieb, Ketcheson, and Shu, High order strong stability preserving time discretizations, J Scientific Computing, 2009. |
Level:beginner
Location:src/ts/impls/explicit/ssp/ssp.c
Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages