:orphan:
# PetscFEIntegrateBdJacobian
Produce the boundary element Jacobian for a chunk of elements by quadrature integration 
## Synopsis
```
#include "petscfe.h" 
PetscErrorCode PetscFEIntegrateBdJacobian(PetscDS ds, PetscWeakForm wf, PetscFormKey key, PetscInt Ne, PetscFEGeom *fgeom, const PetscScalar coefficients[], const PetscScalar coefficients_t[], PetscDS probAux, const PetscScalar coefficientsAux[], PetscReal t, PetscReal u_tshift, PetscScalar elemMat[])
```
Not Collective


## Input Parameters

- ***ds           -*** The `PetscDS` specifying the discretizations and continuum functions
- ***wf           -*** The PetscWeakForm holding the pointwise functions
- ***key          -*** The (label+value, fieldI*Nf + fieldJ) being integrated
- ***Ne           -*** The number of elements in the chunk
- ***fgeom        -*** The face geometry for each cell in the chunk
- ***coefficients -*** The array of FEM basis coefficients for the elements for the Jacobian evaluation point
- ***coefficients_t -*** The array of FEM basis time derivative coefficients for the elements
- ***probAux      -*** The `PetscDS` specifying the auxiliary discretizations
- ***coefficientsAux -*** The array of FEM auxiliary basis coefficients for the elements
- ***t            -*** The time
- ***u_tShift     -*** A multiplier for the dF/du_t term (as opposed to the dF/du term)



## Output Parameter

- ***elemMat              -*** the element matrices for the Jacobian from each element





## Note
```none
  Loop over batch of elements (e):
    Loop over element matrix entries (f,fc,g,gc --> i,j):
      Loop over quadrature points (q):
        Make u_q and gradU_q (loops over fields,Nb,Ncomp)
          elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
                       + \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
                       + \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
                       + \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
```



## See Also
 `PetscFEIntegrateJacobian()`, `PetscFEIntegrateResidual()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/dt/fe/interface/fe.c.html#PetscFEIntegrateBdJacobian">src/dm/dt/fe/interface/fe.c</A>

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/dt/fe/impls/basic/febasic.c.html#PetscFEIntegrateBdJacobian_Basic">PetscFEIntegrateBdJacobian_Basic in src/dm/dt/fe/impls/basic/febasic.c</A><BR>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/dm/dt/fe/interface/fe.c)


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