sfepy.solvers.ts_controllers module

Time step controllers.

class sfepy.solvers.ts_controllers.ElastodynamicsBasicTSC(conf, **kwargs)

Adaptive time step I-controller for elastodynamics.

The implementation is based on [1]. The default parameters correspond to the PID-Controller as implemented in tsc.ed_pid with P=D=0, I=1.

[1] Grafenhorst, Matthias, Joachim Rang, and Stefan Hartmann. “Time-Adaptive Finite Element Simulations of Dynamical Problems for Temperature-Dependent Materials.” Journal of Mechanics of Materials and Structures 12, no. 1 (November 26, 2016): 57–91. https://doi.org/10.2140/jomms.2017.12.57.

Kind: ‘tsc.ed_basic’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

eps_rlist of floats or float

Relative tolerance(s).

eps_alist of floats or float

Absolute tolerance(s).

fminfloat (default: 0.3)

Minimum step size change factor on step rejection.

fmaxfloat (default: 2.5)

Maximum step size change factor on step acceptance.

fsafetyfloat (default: 0.8)

Step size change safety factor.

error_orderfloat (default: 2)

The order of the solver error estimate.

guess_dt0bool (default: False)

Guess a good initial step size from initial conditions.

get_initial_dt(ts, vec, unpack, **kwargs)

Adapted from [1] for second order ODEs.

[1] Hairer, Ernst, Gerhard Wanner, and Syvert P. Nørsett. Solving Ordinary Differential Equations I: Nonstiff Problems. Vol. 8. Springer Series in Computational Mathematics. Berlin, Heidelberg: Springer, 1993. https://doi.org/10.1007/978-3-540-78862-1.

static get_scaled_errors(dt, vec0, vec1, eps_as, eps_rs, unpack)

name = 'tsc.ed_basic'

class sfepy.solvers.ts_controllers.ElastodynamicsLinearTSC(conf, **kwargs)

Adaptive time step controller for elastodynamics and linear problems.

Simple heuristics around ElastodynamicsBasicTSC that increases the step size only after a sufficient number of accepted iterations passed and the increase is large enough. In particular:

• Let new_dt be the step size proposed by tsc.ed_basic and dt the current step size.

• If the current step is rejected, the count attribute is reset to zero and fred * new_dt is returned.

• If the current step is accepted:

  • If the count is lower than inc_wait, it is incremented and dt is returned.

  • Otherwise, if (new_dt / dt) >= min_finc (>= 1), the count is reset to zero and new_dt is returned.

  • Else, if (new_dt / dt) < min_finc, dt is returned.

Kind: ‘tsc.ed_linear’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

eps_rlist of floats or float

Relative tolerance(s).

eps_alist of floats or float

Absolute tolerance(s).

fminfloat (default: 0.3)

Minimum step size change factor on step rejection.

fmaxfloat (default: 2.5)

Maximum step size change factor on step acceptance.

fsafetyfloat (default: 0.8)

Step size change safety factor.

error_orderfloat (default: 2)

The order of the solver error estimate.

guess_dt0bool (default: False)

Guess a good initial step size from initial conditions.

fredfloat (default: 1.0)

Additional step size reduction factor w.r.t. tsc.ed_basic.

inc_waitint (default: 10)

The number of consecutive accepted steps to wait before increasing the step size.

min_fincfloat >= 1 (default: 1.5)

Minimum step size increase factor.

name = 'tsc.ed_linear'

class sfepy.solvers.ts_controllers.ElastodynamicsPIDTSC(conf, **kwargs)

Adaptive time step PID controller for elastodynamics.

The implementation is based on [1], [2] (PI Controller) and [3] (PID). The default parameters correspond to the I-Controller as implemented in tsc.ed_basic.

[1] Grafenhorst, Matthias, Joachim Rang, and Stefan Hartmann. “Time-Adaptive Finite Element Simulations of Dynamical Problems for Temperature-Dependent Materials.” Journal of Mechanics of Materials and Structures 12, no. 1 (November 26, 2016): 57–91. https://doi.org/10.2140/jomms.2017.12.57. [2] Hairer, Ernst, Syvert Paul Nørsett, and Gerhard Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Science & Business Media, 1993. [3] Söderlind, Gustaf. “Digital Filters in Adaptive Time-Stepping.” ACM Transactions on Mathematical Software 29, no. 1 (March 1, 2003): 1–26. https://doi.org/10.1145/641876.641877.

Kind: ‘tsc.ed_pid’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

eps_rlist of floats or float

Relative tolerance(s).

eps_alist of floats or float

Absolute tolerance(s).

fminfloat (default: 0.3)

Minimum step size change factor on step rejection.

fmaxfloat (default: 2.5)

Maximum step size change factor on step acceptance.

fsafetyfloat (default: 0.8)

Step size change safety factor.

error_orderfloat (default: 2)

The order of the solver error estimate.

guess_dt0bool (default: False)

Guess a good initial step size from initial conditions.

pcoeffloat (default: 0.0)

Proportional (P) coefficient of the step size control.

icoeffloat (default: 1.0)

Intregral (I) coefficient of the step size control.

dcoeffloat (default: 0.0)

Derivative (D) coefficient of the step size control.

name = 'tsc.ed_pid'

class sfepy.solvers.ts_controllers.FixedTSC(conf, **kwargs)

Fixed (do-nothing) time step controller.

Kind: ‘tsc.fixed’

For common configuration parameters, see Solver.

Specific configuration parameters:

name = 'tsc.fixed'

class sfepy.solvers.ts_controllers.TimesSequenceTSC(conf, **kwargs)

Given times sequence time step controller.

Kind: ‘tsc.time_sequence’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

timesiterable (default: range(1, 6))

A sequence of times to generate.

get_initial_dt(ts, vec, **kwargs)

name = 'tsc.time_sequence'

sfepy.solvers.ts_controllers.eval_scaled_norm(terr, eps_a, eps_r)