Summary of Time Integrators Available In PETSc#

Table 1 Time integration schemes#

TS Name

Reference

Class

Type

Order

euler

forward Euler

one-step

explicit

11

ssp

multistage SSP [Ket08]

Runge-Kutta

explicit

4\le 4

rk*

multiscale

Runge-Kutta

explicit

1\ge 1

beuler

backward Euler

one-step

implicit

11

cn

Crank-Nicolson

one-step

implicit

22

theta*

theta-method

one-step

implicit

2\le 2

alpha

alpha-method [JWH00]

one-step

implicit

22

gl

general linear [BJW07]

multistep-multistage

implicit

3\le 3

eimex

extrapolated IMEX [CS10]

one-step

IMEX

1\ge 1, adaptive

arkimex

See IMEX Runge-Kutta schemes

IMEX Runge-Kutta

IMEX

151-5

rosw

See Rosenbrock W-schemes

Rosenbrock-W

linearly implicit

141-4

glee

See GL schemes with global error estimation

GL with global error

explicit and implicit

131-3

mprk

Multirate Partitioned Runge-Kutta

multirate

explicit

232-3

basicsymplectic

Basic symplectic integrator for separable Hamiltonian

semi-implicit Euler and Velocity Verlet

explicit

121-2

irk

fully implicit Runge-Kutta

Gauss-Legrendre

implicit

2s2s

BJW07

J.C. Butcher, Z. Jackiewicz, and W.M. Wright. Error propagation of general linear methods for ordinary differential equations. Journal of Complexity, 23(4-6):560–580, 2007. doi:10.1016/j.jco.2007.01.009.

CS10

E.M. Constantinescu and A. Sandu. Extrapolated implicit-explicit time stepping. SIAM Journal on Scientific Computing, 31(6):4452–4477, 2010. doi:10.1137/080732833.

JWH00

K.E. Jansen, C.H. Whiting, and G.M. Hulbert. A generalized-alpha method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering, 190(3):305–319, 2000.

Ket08

D.I. Ketcheson. Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM Journal on Scientific Computing, 30(4):2113–2136, 2008. doi:10.1137/07070485X.