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# PetscDSSetRHSResidual

Set the pointwise residual function for explicit timestepping for a given test field

## Synopsis

    #include "petscds.h"
    PetscErrorCode PetscDSSetRHSResidual(PetscDS ds, PetscInt f, void (*f0)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]), void (*f1)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))

Not Collective

## Input Parameters

- ds - The `PetscDS`

- f - The test field number

- f0 - integrand for the test function term

- f1 - integrand for the test function gradient term

## Calling sequence for the callbacks `f0`

- dim - the spatial dimension

- Nf - the number of fields

- NfAux - the number of auxiliary fields

- uOff - the offset into u[] and u_t[] for each field

- uOff_x - the offset into u_x[] for each field

- u - each field evaluated at the current point

- u_t - the time derivative of each field evaluated at the current point

- u_x - the gradient of each field evaluated at the current point

- aOff - the offset into a[] and a_t[] for each auxiliary field

- aOff_x - the offset into a_x[] for each auxiliary field

- a - each auxiliary field evaluated at the current point

- a_t - the time derivative of each auxiliary field evaluated at the current point

- a_x - the gradient of auxiliary each field evaluated at the current point

- t - current time

- x - coordinates of the current point

- numConstants - number of constant parameters

- constants - constant parameters

- f0 - output values at the current point

## Note

`f1` has an identical form and is omitted for brevity.

We are using a first order FEM model for the weak form: \( \int_\Omega \phi f_0(u, u_t, \nabla u, x, t) + \nabla\phi \cdot {\vec f}_1(u, u_t, \nabla u, x, t)\)

## See Also

`PetscDS`, `PetscDSGetResidual()`

## Level

intermediate

## Location

src/dm/dt/interface/dtds.c

## Examples

src/ts/tutorials/ex45.c

Index of all DT routines
Table of Contents for all manual pages
Index of all manual pages