PETSc version 3.17.4
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# PetscFEIntegrateJacobian

Produce the element Jacobian for a chunk of elements by quadrature integration

### Synopsis

    #include "petscfe.h"
    PetscErrorCode PetscFEIntegrateJacobian(PetscDS ds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom,
                                            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
| jtype | - The type of matrix pointwise functions that should be used
| key | - The (label+value, fieldI*Nf + fieldJ) being integrated
| s | - The side of the cell being integrated, 0 for negative and 1 for positive
| Ne | - The number of elements in the chunk
| cgeom | - The cell 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

    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

PetscFEIntegrateResidual()

### Level

intermediate

### Location

src/dm/dt/fe/interface/fe.c

### Implementations

src/dm/dt/fe/impls/basic/febasic.c:655:PetscErrorCode PetscFEIntegrateJacobian_Basic(PetscDS ds, PetscFEJacobianType jtype, PetscFormKey key, PetscInt Ne, PetscFEGeom *cgeom,
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