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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
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<A NAME="PetscFEIntegrateJacobian"><H1>PetscFEIntegrateJacobian</H1></A>
Produce the element Jacobian for a chunk of elements by quadrature integration
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscfe.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../DM/PetscFEIntegrateJacobian.html#PetscFEIntegrateJacobian">PetscFEIntegrateJacobian</A>(<A HREF="../DM/PetscFE.html#PetscFE">PetscFE</A> fem, <A HREF="../DM/PetscDS.html#PetscDS">PetscDS</A> prob, <A HREF="../DM/PetscFEJacobianType.html#PetscFEJacobianType">PetscFEJacobianType</A> jtype, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> fieldI, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> fieldJ, <A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> Ne, PetscFEGeom *cgeom,
const <A HREF="../Sys/PetscScalar.html#PetscScalar">PetscScalar</A> coefficients[], const <A HREF="../Sys/PetscScalar.html#PetscScalar">PetscScalar</A> coefficients_t[], <A HREF="../DM/PetscDS.html#PetscDS">PetscDS</A> probAux, const <A HREF="../Sys/PetscScalar.html#PetscScalar">PetscScalar</A> coefficientsAux[], <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> t, <A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> u_tshift, <A HREF="../Sys/PetscScalar.html#PetscScalar">PetscScalar</A> elemMat[])
</PRE>
Not collective
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>fem </B></TD><TD>- The <A HREF="../DM/PetscFE.html#PetscFE">PetscFE</A> object for the field being integrated
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>prob </B></TD><TD>- The <A HREF="../DM/PetscDS.html#PetscDS">PetscDS</A> specifying the discretizations and continuum functions
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>jtype </B></TD><TD>- The type of matrix pointwise functions that should be used
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>fieldI </B></TD><TD>- The test field being integrated
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>fieldJ </B></TD><TD>- The basis field being integrated
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>Ne </B></TD><TD>- The number of elements in the chunk
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>cgeom </B></TD><TD>- The cell geometry for each cell in the chunk
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>coefficients </B></TD><TD>- The array of FEM basis coefficients for the elements for the Jacobian evaluation point
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>coefficients_t </B></TD><TD>- The array of FEM basis time derivative coefficients for the elements
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>probAux </B></TD><TD>- The <A HREF="../DM/PetscDS.html#PetscDS">PetscDS</A> specifying the auxiliary discretizations
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>coefficientsAux </B></TD><TD>- The array of FEM auxiliary basis coefficients for the elements
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>t </B></TD><TD>- The time
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>u_tShift </B></TD><TD>- A multiplier for the dF/du_t term (as opposed to the dF/du term)
</TD></TR></TABLE>
<P>
Output Parameter
<DT><B>elemMat </B> -the element matrices for the Jacobian from each element
<br>
<P>
<H3><FONT COLOR="#CC3333">Note</FONT></H3>
<pre>
Loop over batch of elements (e):
</pre>
<pre>
Loop over element matrix entries (f,fc,g,gc --> i,j):
</pre>
<pre>
Loop over quadrature points (q):
</pre>
<pre>
Make u_q and gradU_q (loops over fields,Nb,Ncomp)
</pre>
<pre>
elemMat[i,j] += \psi^{fc}_f(q) g0_{fc,gc}(u, \nabla u) \phi^{gc}_g(q)
</pre>
<pre>
+ \psi^{fc}_f(q) \cdot g1_{fc,gc,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
</pre>
<pre>
+ \nabla\psi^{fc}_f(q) \cdot g2_{fc,gc,df}(u, \nabla u) \phi^{gc}_g(q)
</pre>
<pre>
+ \nabla\psi^{fc}_f(q) \cdot g3_{fc,gc,df,dg}(u, \nabla u) \nabla\phi^{gc}_g(q)
</pre>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../DM/PetscFEIntegrateResidual.html#PetscFEIntegrateResidual">PetscFEIntegrateResidual</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>developer<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/dm/dt/fe/interface/fe.c.html#PetscFEIntegrateJacobian">src/dm/dt/fe/interface/fe.c</A>
<P><H3><FONT COLOR="CC3333">Implementations</FONT></H3>src/dm/dt/fe/impls/basic/febasic.c:577:PetscErrorCode PetscFEIntegrateJacobian_Basic(PetscFE fem, PetscDS prob, PetscFEJacobianType jtype, PetscInt fieldI, PetscInt fieldJ, PetscInt Ne, PetscFEGeom *geom,
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