File imex-bdf2.hxx¶

class IMEXBDF2 : public Solver ¶

#include <imex-bdf2.hxx>

IMEX-BDF2 time integration solver

Scheme taken from this paper: http://homepages.cwi.nl/~willem/DOCART/JCP07.pdf

W.Hundsdorfer, S.J.Ruuth “IMEX extensions of linear multistep methods with general

monotonicity and boundedness properties” JCP 225 (2007) 2016-2042

The method has been extended to variable order, variable timestep, and includes some adaptive capabilities

Public Functions

IMEXBDF2(Options *opt = nullptr)¶

~IMEXBDF2()¶

inline virtual BoutReal getCurrentTimestep() override¶: Returns the current internal timestep.

virtual int init(int nout, BoutReal tstep) override¶

Initialise solver. Must be called once and only once

Initialisation routine. Called once before solve.

Parameters

nout – [in] Number of outputs
tstep – [in] Time between outputs. NB: Not internal timestep

virtual int run() override¶: Run the simulation.

PetscErrorCode snes_function(Vec x, Vec f, bool linear)¶

Nonlinear function. This is called by PETSc SNES object via a static C-style function. For implicit time integration this function calculates:

f = (x - gamma*G(x)) - rhs

Parameters

x – [in] The state vector
f – [out] The vector for the result f(x)
linear – [in] Specifies that the SNES solver is in a linear (KSP) inner loop, so the operator should be linearised if possible

PetscErrorCode precon(Vec x, Vec f)¶

Preconditioner. Called by PCapply via a C-style static function.

Parameters

x – [in] The vector to be operated on
f – [out] The result of the operation

Private Functions

void take_step(BoutReal curtime, BoutReal dt, int order = 2)¶

Take a full step at requested order

Take a full IMEX-BDF step of order “order”. Note that this assumes that enough time points are already available (in u and f).

Inputs: u* - Solution history f* - Non-stiff component history

Outputs: u - Latest Solution f1 - Non-stiff time derivative at current time

Parameters

curtime – [in] The current simulation time
dt – [in] The time step to take
order – [in] The order of accuracy

void constructSNES(SNES *snesIn)¶: Setup a SNES object This includes creating, setting functions, options, and internal (KSP) solver, and Jacobian options including coloring.

void shuffleState()¶: Shuffle state along one step.

void calculateCoeffs(int order)¶: Populate the *Fac vectors and dtImp with appropriate coefficients for this order.

PetscErrorCode solve_implicit(BoutReal curtime, BoutReal gamma)¶

template<class Op> void loopVars(BoutReal *u)¶: Loop over arrays, using template parameter to specify the operation to be performed at each point

void saveVars(BoutReal *u)¶

Save variables from BOUT++ fields into a pre-allocated array u

Copy data from fields into array

void loadVars(BoutReal *u)¶

Load variables from input vector u into BOUT++ fields.

Copy data from array into fields

void saveDerivs(BoutReal *u)¶

Save time derivatives from ddt() fields into a preallocated array u.

Copy time derivatives from fields into array

Private Members

int maxOrder¶: Specify the maximum order of the scheme to use (1/2/3)

BoutReal out_timestep¶: The output timestep.

int nsteps¶: Number of output steps.

BoutReal timestep¶: The internal timestep.

int ninternal¶: Number of internal steps per output.

int mxstep¶: Maximum number of internal steps between outputs.

bool adaptive¶: Use adaptive timestepping?

int nadapt¶: How often do we check the error.

int mxstepAdapt¶: Maximum no. consecutive times we try to reduce timestep.

BoutReal scaleCushUp¶: Don’t increase timestep if scale factor < 1.0+scaleCushUp.

BoutReal scaleCushDown¶: Don’t decrease timestep if scale factor > 1.0-scaleCushDown.

BoutReal adaptRtol¶: Target relative error for adaptivity.

BoutReal dtMin¶: Minimum timestep we want to use.

BoutReal dtMax¶: Maximum timestep we want to use.

BoutReal dtMinFatal¶: If timestep wants to drop below this we abort. Set -ve to deactivate

std::vector<BoutReal> uFac¶

std::vector<BoutReal> fFac¶

std::vector<BoutReal> gFac¶

BoutReal dtImp¶

int nlocal¶

int neq¶: Number of variables on local processor and in total.

Array<BoutReal> u¶: System state at current time.

std::vector<Array<BoutReal>> uV¶: The solution history.

std::vector<Array<BoutReal>> fV¶: The non-stiff solution history.

std::vector<BoutReal> timesteps¶: Timestep history.

Array<BoutReal> rhs¶

Array<BoutReal> err¶

BoutReal implicit_gamma¶

BoutReal implicit_curtime¶

int predictor¶: Predictor method.

PetscLib lib¶: Handles initialising, finalising PETSc.

Vec snes_f¶: Used by SNES to store function.

Vec snes_x¶: Result of SNES.

SNES snes¶: SNES context.

SNES snesAlt¶: Alternative SNES object for adaptive checks.

SNES snesUse¶: The snes object to use in solve stage. Allows easy switching.

Mat Jmf¶: Matrix-free Jacobian.

bool diagnose¶: Output diagnostics every timestep.

bool verbose¶: Gives a more verbose output for each timestep.

int linear_fails¶: Number of linear (KSP) convergence failures.

int nonlinear_fails¶: Numbef of nonlinear (SNES) convergence failures.

bool have_constraints¶: Are there any constraint variables?

Array<BoutReal> is_dae¶: If using constraints, 1 -> DAE, 0 -> AE.

MatFDColoring fdcoloring¶: Matrix coloring context, used for finite difference Jacobian evaluation

Private Static Attributes

static constexpr int MAX_SUPPORTED_ORDER = 4¶