# 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):
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)


PetscFEIntegrateResidual()

intermediate

## Location#

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

Edit on GitLab