3.4.5.1. A skeleton of the user’s main program
The following is a skeleton of the user’s main program (or calling program) for the integration of an ODE IVP using the MRIStep module. Most of the steps are independent of the NVECTOR, SUNMATRIX, SUNLINSOL and SUNNONLINSOL implementations used. For the steps that are not, refer to §9, §10, §11, and §12 for the specific name of the function to be called or macro to be referenced.
Initialize parallel or multi-threaded environment, if appropriate.
For example, call
MPI_Init
to initialize MPI if used, or setnum_threads
, the number of threads to use within the threaded vector functions, if used.Create the SUNDIALS context object
Call
SUNContext_Create()
to allocate theSUNContext
object.Set problem dimensions, etc.
This generally includes the problem size,
N
, and may include the local vector lengthNlocal
.Note
The variables
N
andNlocal
should be of typesunindextype
.Set vector of initial values
To set the vector
y0
of initial values, use the appropriate functions defined by the particular NVECTOR implementation.For native SUNDIALS vector implementations (except the CUDA and RAJA based ones), use a call of the form
y0 = N_VMake_***(..., ydata);
if the
sunrealtype
arrayydata
containing the initial values of \(y\) already exists. Otherwise, create a new vector by making a call of the formy0 = N_VNew_***(...);
and then set its elements by accessing the underlying data where it is located with a call of the form
ydata = N_VGetArrayPointer_***(y0);
For details on each of SUNDIALS’ provided vector implementations, see the corresponding sections in §9 for details.
Create an inner stepper object to solve the fast (inner) IVP
If using ARKStep as the fast (inner) integrator, create the ARKStep object with
ARKStepCreate()
and configure the integrator as desired for evolving the fast time scale. See sections §3.4.2.1 and §3.4.2.2.8 for details on configuring ARKStep.Once the ARKStep object is setup, create an
MRIStepInnerStepper
object withARKStepCreateMRIStepInnerStepper()
.If supplying a user-defined fast (inner) integrator, create the
MRIStepInnerStepper
object as described in section §3.4.5.4.
Note
When using ARKStep as a fast (inner) integrator it is the user’s responsibility to create, configure, and attach the integrator to the MRIStep module. User-specified options regarding how this fast integration should be performed (e.g., adaptive vs. fixed time step, explicit/implicit/ImEx partitioning, algebraic solvers, etc.) will be respected during evolution of the fast time scale during MRIStep integration.
Due to the algorithms supported in MRIStep, the ARKStep module used for the fast time scale must be configured with an identity mass matrix.
If a user_data pointer needs to be passed to user functions called by the fast (inner) integrator then it should be attached here by calling
ARKStepSetUserData()
. This user_data pointer will only be passed to user-supplied functions that are attached to the fast (inner) integrator. To supply a user_data pointer to user-supplied functions called by the slow (outer) integrator the desired pointer should be attached by callingMRIStepSetUserData()
after creating the MRIStep memory below. The user_data pointers attached to the inner and outer integrators may be the same or different depending on what is required by the user code.Specifying a rootfinding problem for the fast integration is not supported. Rootfinding problems should be created and initialized with the slow integrator. See the steps below and
MRIStepRootInit()
for more details.Create an MRIStep object for the slow (outer) integration
Create the MRIStep object by calling
MRIStepCreate()
. One of the inputs toMRIStepCreate()
is theMRIStepInnerStepper
object for solving the fast (inner) IVP created in the previous step.Set the slow step size
Call
MRIStepSetFixedStep()
to specify the slow time step size.Create and configure implicit solvers (as appropriate)
Specifically, if MRIStep is configured with an implicit slow right-hand side function in the prior step, then the following steps are recommended:
Specify integration tolerances
Call
MRIStepSStolerances()
orMRIStepSVtolerances()
to specify either a scalar relative tolerance and scalar absolute tolerance, or a scalar relative tolerance and a vector of absolute tolerances, respectively. Alternatively, callMRIStepWFtolerances()
to specify a function which sets directly the weights used in evaluating WRMS vector norms. See §3.4.5.2.2 for details.Create nonlinear solver object
If a non-default nonlinear solver object is desired for implicit MRI stage solves (see §3.4.5.2.4), then that nonlinear solver object must be created by using the appropriate functions defined by the particular SUNNONLINSOL implementation (e.g.,
NLS = SUNNonlinSol_***(...);
where***
is the name of the nonlinear solver (see §12 for details).For the SUNDIALS-supplied SUNNONLINSOL implementations, the nonlinear solver object may be created using a call of the form
SUNNonlinearSolver NLS = SUNNonlinSol_*(...);
where
*
can be replaced with “Newton”, “FixedPoint”, or other options, as discussed in the sections §3.4.2.2.5 and §12.Note: by default, MRIStep will use the Newton nonlinear solver (see section §12.7), so a custom nonlinear solver object is only needed when using a different solver, or for the user to exercise additional controls over the Newton solver.
Attach nonlinear solver module
If a nonlinear solver object was created above, then it must be attached to MRIStep using the call (for details see §3.4.5.2.4):
ier = MRIStepSetNonlinearSolver(...);
Set nonlinear solver optional inputs
Call the appropriate set functions for the selected nonlinear solver module to change optional inputs specific to that nonlinear solver. These must be called after attaching the nonlinear solver to MRIStep, otherwise the optional inputs will be overridden by MRIStep defaults. See §12 for more information on optional inputs.
Create matrix object
If a nonlinear solver requiring a linear solver will be used (e.g., a Newton iteration) and if that linear solver will be matrix-based, then a template Jacobian matrix must be created by using the appropriate functions defined by the particular SUNMATRIX implementation.
For the SUNDIALS-supplied SUNMATRIX implementations, the matrix object may be created using a call of the form
SUNMatrix A = SUNBandMatrix(...);
or similar for other matrix modules (see §10 for further information).
Create linear solver object
If a nonlinear solver requiring a linear solver will be used (e.g., a Newton iteration), then the desired linear solver object(s) must be created by using the appropriate functions defined by the particular SUNLINSOL implementation.
For any of the SUNDIALS-supplied SUNLINSOL implementations, the linear solver object may be created using a call of the form
SUNLinearSolver LS = SUNLinSol_*(...);
where
*
can be replaced with “Dense”, “SPGMR”, or other options, as discussed in §11.Set linear solver optional inputs
Call
*Set*
functions from the selected linear solver module to change optional inputs specific to that linear solver. See the documentation for each SUNLINSOL module in §11 for details.Attach linear solver module
If a linear solver was created above for implicit MRI stage solves, initialize the ARKLS linear solver interface by attaching the linear solver object (and Jacobian matrix object, if applicable) with the call (for details see §3.4.5.2.3):
ier = MRIStepSetLinearSolver(...);
Set optional inputs
Call
MRIStepSet*
functions to change any optional inputs that control the behavior of MRIStep from their default values. See §3.4.5.2.7 for details.Specify rootfinding problem
Optionally, call
MRIStepRootInit()
to initialize a rootfinding problem to be solved during the integration of the ODE system. See §3.4.5.2.5 for general details, and §3.4.5.2.7 for relevant optional input calls.Advance solution in time
For each point at which output is desired, call
ier = MRIStepEvolve(arkode_mem, tout, yout, &tret, itask);
Here,
itask
specifies the return mode. The vectoryout
(which can be the same as the vectory0
above) will contain \(y(t_\text{out})\). See §3.4.5.2.6 for details.Get optional outputs
Call
MRIStepGet*
and/orARKStepGet*
functions to obtain optional output from the slow or fast integrators respectively. See §3.4.5.2.9 and §3.4.2.2.10 for details.Deallocate memory for solution vector
Upon completion of the integration, deallocate memory for the vector
y
(oryout
) by calling the NVECTOR destructor function:N_VDestroy(y);
Free solver memory
If ARKStep was used as the fast (inner) IVP integrator, call
MRIStepInnerStepper_Free()
andARKStepFree()
to free the memory allocated for the fast (inner) integrator.If a user-defined fast (inner) integrator was supplied, free the integrator content and call
MRIStepInnerStepper_Free()
to free theMRIStepInnerStepper
object.Call
MRIStepFree()
to free the memory allocated for the slow integration object.
Free linear solver and matrix memory (as appropriate)
Call
SUNLinSolFree()
and (possibly)SUNMatDestroy()
to free any memory allocated for any linear solver and/or matrix objects created above for either the fast or slow integrators.Free nonlinear solver memory (as appropriate)
If a user-supplied
SUNNonlinearSolver
was provided to MRIStep, then callSUNNonlinSolFree()
to free any memory allocated for the nonlinear solver object created above.Free the SUNContext object Call
SUNContext_Free()
to free the memory allocated for theSUNContext
object.
Finalize MPI, if used
Call
MPI_Finalize
to terminate MPI.