# 3.4.4.1. 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 set`num_threads`

, the number of threads to use within the threaded vector functions, if used.Create the SUNDIALS context object

Call

`SUNContext_Create()`

to allocate the`SUNContext`

object.Set problem dimensions, etc.

This generally includes the problem size,

`N`

, and may include the local vector length`Nlocal`

.Note

The variables

`N`

and`Nlocal`

should be of type`sunindextype`

.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

`realtype`

array`ydata`

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 with`ARKStepCreateMRIStepInnerStepper()`

.If supplying a user-defined fast (inner) integrator, create the

`MRIStepInnerStepper`

object as described in section §3.4.4.4.

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 calling`MRIStepSetUserData()`

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 to`MRIStepCreate()`

is the`MRIStepInnerStepper`

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()`

or`MRIStepSVtolerances()`

to specify either a scalar relative tolerance and scalar absolute tolerance, or a scalar relative tolerance and a vector of absolute tolerances, respectively. Alternatively, call`MRIStepWFtolerances()`

to specify a function which sets directly the weights used in evaluating WRMS vector norms. See §3.4.4.2.2 for details.Create nonlinear solver object

If a non-default nonlinear solver object is desired for implicit MRI stage solves (see §3.4.4.2.4), 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 §3.4.4.2.4):

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 §3.4.4.2.3):

ier = MRIStepSetLinearSolver(...);

Set optional inputs

Call

`MRIStepSet*`

functions to change any optional inputs that control the behavior of MRIStep from their default values. See §3.4.4.2.7 for details.Specify rootfinding problem

Optionally, call

`MRIStepRootInit()`

to initialize a rootfinding problem to be solved during the integration of the ODE system. See §3.4.4.2.5 for general details, and §3.4.4.2.7 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 vector`yout`

(which can be the same as the vector`y0`

above) will contain \(y(t_\text{out})\). See §3.4.4.2.6 for details.Get optional outputs

Call

`MRIStepGet*`

and/or`ARKStepGet*`

functions to obtain optional output from the slow or fast integrators respectively. See §3.4.4.2.9 and §3.4.2.2.10 for details.Deallocate memory for solution vector

Upon completion of the integration, deallocate memory for the vector

`y`

(or`yout`

) 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()`

and`ARKStepFree()`

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 the`MRIStepInnerStepper`

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 call`SUNNonlinSolFree()`

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 the`SUNContext`

object.

Finalize MPI, if used

Call

`MPI_Finalize`

to terminate MPI.