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


#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


  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_Basic in src/dm/dt/fe/impls/basic/febasic.c

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