PetscFEIntegrateHybridJacobian#

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

Synopsis#

#include "petscfe.h" 
PetscErrorCode PetscFEIntegrateHybridJacobian(PetscDS ds, PetscDS dsIn, PetscFEJacobianType jtype, PetscFormKey key, PetscInt s, 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 for the output
dsIn - The PetscDS specifying the discretizations and continuum functions for the input
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
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#

  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)