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<center><a href="https://gitlab.com/petsc/petsc/-/blob/966382dc56242773704ef5f5cee7aa2db3ebc577/include/petscdualspace.h">Actual source code: petscdualspace.h</a></center><br>
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<a name="line1"> 1: </a><font color="#B22222">/*</font>
<a name="line2"> 2: </a><font color="#B22222"> Objects which encapsulate finite element spaces</font>
<a name="line3"> 3: </a><font color="#B22222">*/</font>
<a name="line4"> 4: </a><font color="#A020F0">#pragma once</font>
<a name="line5"> 5: </a>#include <A href="../include/petscdm.h.html"><petscdm.h></A>
<a name="line6"> 6: </a>#include <A href="../include/petscdt.h.html"><petscdt.h></A>
<a name="line7"> 7: </a>#include <A href="../include/petscfetypes.h.html"><petscfetypes.h></A>
<a name="line8"> 8: </a>#include <A href="../include/petscdstypes.h.html"><petscdstypes.h></A>
<a name="line9"> 9: </a>#include <A href="../include/petscspace.h.html"><petscspace.h></A>
<a name="line11"> 11: </a><font color="#B22222">/* MANSEC = <a href="../manualpages/DM/DM.html">DM</a> */</font>
<a name="line12"> 12: </a><font color="#B22222">/* SUBMANSEC = DUALSPACE */</font>
<a name="line14"> 14: </a><font color="#B22222">/*S</font>
<a name="line15"> 15: </a><font color="#B22222"> <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> - PETSc object that manages the dual space to a linear space, e.g. the space of evaluation functionals at the vertices of a triangle</font>
<a name="line17"> 17: </a><font color="#B22222"> Level: beginner</font>
<a name="line19"> 19: </a><font color="#B22222">.seealso: `<a href="../manualpages/DUALSPACE/PetscDualSpaceCreate.html">PetscDualSpaceCreate</a>()`, `<a href="../manualpages/SPACE/PetscSpace.html">PetscSpace</a>`, `<a href="../manualpages/SPACE/PetscSpaceCreate.html">PetscSpaceCreate</a>()`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetType.html">PetscDualSpaceSetType</a>()`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a>`</font>
<a name="line20"> 20: </a><font color="#B22222">S*/</font>
<a name="line21"> 21: </a><font color="#4169E1">typedef struct _p_PetscDualSpace *<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>;</font>
<a name="line23"> 23: </a><font color="#B22222">/*MC</font>
<a name="line24"> 24: </a><font color="#B22222"> <a href="../manualpages/DUALSPACE/PetscDualSpaceReferenceCell.html">PetscDualSpaceReferenceCell</a> - The type of reference cell</font>
<a name="line26"> 26: </a><font color="#B22222"> Level: beginner</font>
<a name="line28"> 28: </a><font color="#B22222"> Note:</font>
<a name="line29"> 29: </a><font color="#B22222"> This is used only for automatic creation of reference cells. A `<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>` can accept an arbitrary `<a href="../manualpages/DM/DM.html">DM</a>` for a reference cell.</font>
<a name="line31"> 31: </a><font color="#B22222">.seealso: `<a href="../manualpages/SPACE/PetscSpace.html">PetscSpace</a>`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceCreate.html">PetscDualSpaceCreate</a>()`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a>`</font>
<a name="line32"> 32: </a><font color="#B22222">M*/</font>
<a name="line33"> 33: </a><font color="#4169E1">typedef</font> <font color="#4169E1">enum</font> {
<a name="line34"> 34: </a> PETSCDUALSPACE_REFCELL_SIMPLEX,
<a name="line35"> 35: </a> PETSCDUALSPACE_REFCELL_TENSOR
<a name="line36"> 36: </a>} <a href="../manualpages/DUALSPACE/PetscDualSpaceReferenceCell.html">PetscDualSpaceReferenceCell</a>;
<a name="line37"> 37: </a>PETSC_EXTERN const char *const PetscDualSpaceReferenceCells[];
<a name="line39"> 39: </a><font color="#B22222">/*MC</font>
<a name="line40"> 40: </a><font color="#B22222"> <a href="../manualpages/DUALSPACE/PetscDualSpaceTransformType.html">PetscDualSpaceTransformType</a> - The type of function transform</font>
<a name="line42"> 42: </a><font color="#B22222"> Values:</font>
<a name="line43"> 43: </a><font color="#B22222">+ `IDENTITY_TRANSFORM` - make no changes in the function</font>
<a name="line44"> 44: </a><font color="#B22222">. `COVARIANT_PIOLA_TRANSFORM` - Covariant Piola: $\sigma^*(F) = J^{-T} F \circ \phi^{-1)$</font>
<a name="line45"> 45: </a><font color="#B22222">- `CONTRAVARIANT_PIOLA_TRANSFORM` - Contravariant Piola: $\sigma^*(F) = 1/|J| J F \circ \phi^{-1)$</font>
<a name="line47"> 47: </a><font color="#B22222"> Level: intermediate</font>
<a name="line49"> 49: </a><font color="#B22222"> Note:</font>
<a name="line50"> 50: </a><font color="#B22222"> These transforms, and their inverses, are used to move functions and functionals between the reference element and real space.</font>
<a name="line51"> 51: </a><font color="#B22222"> Suppose that we have a mapping $\phi$ which maps the reference cell to real space, and its Jacobian $J$. If we want to transform function $F$ on the reference element,</font>
<a name="line52"> 52: </a><font color="#B22222"> so that it acts on real space, we use the pushforward transform $\sigma^*$. The pullback $\sigma_*$ is the inverse transform.</font>
<a name="line53"> 53: </a><font color="#B22222"> {cite}`rogneskirbylogg2009`</font>
<a name="line55"> 55: </a><font color="#B22222">.seealso: `<a href="../manualpages/DUALSPACE/PetscDualSpaceGetDeRahm.html">PetscDualSpaceGetDeRahm</a>()`</font>
<a name="line56"> 56: </a><font color="#B22222">M*/</font>
<a name="line57"> 57: </a><font color="#4169E1">typedef</font> <font color="#4169E1">enum</font> {
<a name="line58"> 58: </a> IDENTITY_TRANSFORM,
<a name="line59"> 59: </a> COVARIANT_PIOLA_TRANSFORM,
<a name="line60"> 60: </a> CONTRAVARIANT_PIOLA_TRANSFORM
<a name="line61"> 61: </a>} <a href="../manualpages/DUALSPACE/PetscDualSpaceTransformType.html">PetscDualSpaceTransformType</a>;
<a name="line63"> 63: </a>PETSC_EXTERN <a href="../manualpages/Sys/PetscClassId.html">PetscClassId</a> PETSCDUALSPACE_CLASSID;
<a name="line65"> 65: </a><font color="#B22222">/*J</font>
<a name="line66"> 66: </a><font color="#B22222"> <a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a> - String with the name of a PETSc dual space</font>
<a name="line68"> 68: </a><font color="#B22222"> Values:</font>
<a name="line69"> 69: </a><font color="#B22222">+ <a href="../manualpages/DUALSPACE/PETSCDUALSPACELAGRANGE.html">PETSCDUALSPACELAGRANGE</a> - a dual space of pointwise evaluation functionals</font>
<a name="line70"> 70: </a><font color="#B22222">. <a href="../manualpages/DUALSPACE/PETSCDUALSPACESIMPLE.html">PETSCDUALSPACESIMPLE</a> - a dual space defined by functionals provided with `<a href="../manualpages/DUALSPACE/PetscDualSpaceSimpleSetFunctional.html">PetscDualSpaceSimpleSetFunctional</a>()`</font>
<a name="line71"> 71: </a><font color="#B22222">. <a href="../manualpages/DUALSPACE/PETSCDUALSPACEREFINED.html">PETSCDUALSPACEREFINED</a> - the joint dual space defined by a group of cells, usually refined from one larger cell</font>
<a name="line72"> 72: </a><font color="#B22222">. <a href="../manualpages/DUALSPACE/PETSCDUALSPACEBDM.html">PETSCDUALSPACEBDM</a> - a dual space for Brezzi-Douglas-Marini elements</font>
<a name="line73"> 73: </a><font color="#B22222">- <a href="../manualpages/DUALSPACE/PETSCDUALSPACESUM.html">PETSCDUALSPACESUM</a> - a dual space that is a sum of other dual spaces</font>
<a name="line75"> 75: </a><font color="#B22222"> Level: beginner</font>
<a name="line77"> 77: </a><font color="#B22222">.seealso: `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetType.html">PetscDualSpaceSetType</a>()`, `<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>`, `<a href="../manualpages/SPACE/PetscSpace.html">PetscSpace</a>`</font>
<a name="line78"> 78: </a><font color="#B22222">J*/</font>
<a name="line79"> 79: </a><font color="#4169E1">typedef const char *<a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a>;</font>
<a name="line80"> 80: </a><strong><font color="#228B22">#define <a href="../manualpages/DUALSPACE/PETSCDUALSPACELAGRANGE.html">PETSCDUALSPACELAGRANGE</a> </font><font color="#666666">"lagrange"</font><font color="#228B22"></font></strong>
<a name="line81"> 81: </a><strong><font color="#228B22">#define <a href="../manualpages/DUALSPACE/PETSCDUALSPACESIMPLE.html">PETSCDUALSPACESIMPLE</a> </font><font color="#666666">"simple"</font><font color="#228B22"></font></strong>
<a name="line82"> 82: </a><strong><font color="#228B22">#define <a href="../manualpages/DUALSPACE/PETSCDUALSPACEREFINED.html">PETSCDUALSPACEREFINED</a> </font><font color="#666666">"refined"</font><font color="#228B22"></font></strong>
<a name="line83"> 83: </a><strong><font color="#228B22">#define <a href="../manualpages/DUALSPACE/PETSCDUALSPACEBDM.html">PETSCDUALSPACEBDM</a> </font><font color="#666666">"bdm"</font><font color="#228B22"></font></strong>
<a name="line84"> 84: </a><strong><font color="#228B22">#define <a href="../manualpages/DUALSPACE/PETSCDUALSPACESUM.html">PETSCDUALSPACESUM</a> </font><font color="#666666">"sum"</font><font color="#228B22"></font></strong>
<a name="line86"> 86: </a><font color="#B22222">/*MC</font>
<a name="line87"> 87: </a><font color="#B22222"> <a href="../manualpages/DUALSPACE/PETSCDUALSPACEBDM.html">PETSCDUALSPACEBDM</a> = "bdm" - A `<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>` object that encapsulates a dual space for Brezzi-Douglas-Marini elements</font>
<a name="line89"> 89: </a><font color="#B22222"> Level: intermediate</font>
<a name="line91"> 91: </a><font color="#B22222"> Note:</font>
<a name="line92"> 92: </a><font color="#B22222"> This type is a constructor alias of `<a href="../manualpages/DUALSPACE/PETSCDUALSPACELAGRANGE.html">PETSCDUALSPACELAGRANGE</a>`. During</font>
<a name="line93"> 93: </a><font color="#B22222"> `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetUp.html">PetscDualSpaceSetUp</a>()`, the correct value of `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetFormDegree.html">PetscDualSpaceSetFormDegree</a>()` is</font>
<a name="line94"> 94: </a><font color="#B22222"> set for H-div conforming spaces. The type of the dual space is then changed to</font>
<a name="line95"> 95: </a><font color="#B22222"> to `<a href="../manualpages/DUALSPACE/PETSCDUALSPACELAGRANGE.html">PETSCDUALSPACELAGRANGE</a>`.</font>
<a name="line97"> 97: </a><font color="#B22222">.seealso: `<a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a>`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceCreate.html">PetscDualSpaceCreate</a>()`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetType.html">PetscDualSpaceSetType</a>()`, `<a href="../manualpages/DUALSPACE/PETSCDUALSPACELAGRANGE.html">PETSCDUALSPACELAGRANGE</a>`, `<a href="../manualpages/DUALSPACE/PetscDualSpaceSetFormDegree.html">PetscDualSpaceSetFormDegree</a>()`</font>
<a name="line98"> 98: </a><font color="#B22222">M*/</font>
<a name="line100">100: </a>PETSC_EXTERN <a href="../manualpages/Sys/PetscFunctionList.html">PetscFunctionList</a> PetscDualSpaceList;
<a name="line101">101: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceCreate.html">PetscDualSpaceCreate</a>(<a href="../manualpages/Sys/MPI_Comm.html">MPI_Comm</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line102">102: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceDestroy.html">PetscDualSpaceDestroy</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line103">103: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceDuplicate.html">PetscDualSpaceDuplicate</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line104">104: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetType.html">PetscDualSpaceSetType</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a>)</font></strong>;
<a name="line105">105: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetType.html">PetscDualSpaceGetType</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DUALSPACE/PetscDualSpaceType.html">PetscDualSpaceType</a> *)</font></strong>;
<a name="line106">106: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetUniform.html">PetscDualSpaceGetUniform</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line107">107: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetNumDof.html">PetscDualSpaceGetNumDof</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> **)</font></strong>;
<a name="line108">108: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetSection.html">PetscDualSpaceGetSection</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a> *)</font></strong>;
<a name="line109">109: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetInteriorSection.html">PetscDualSpaceGetInteriorSection</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/PetscSection/PetscSection.html">PetscSection</a> *)</font></strong>;
<a name="line110">110: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetUp.html">PetscDualSpaceSetUp</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>)</font></strong>;
<a name="line111">111: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetFromOptions.html">PetscDualSpaceSetFromOptions</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>)</font></strong>;
<a name="line112">112: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceViewFromOptions.html">PetscDualSpaceViewFromOptions</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscObject.html">PetscObject</a>, const char[])</font></strong>;
<a name="line114">114: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceView.html">PetscDualSpaceView</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Viewer/PetscViewer.html">PetscViewer</a>)</font></strong>;
<a name="line115">115: </a><strong><font color="#4169E1"><a name="PetscDualSpaceRegister"></a>PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceRegister.html">PetscDualSpaceRegister</a>(const char[], <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> (*)(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>)</font></strong>);
<a name="line116">116: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> PetscDualSpaceRegisterDestroy(void)</font></strong>;
<a name="line118">118: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetDimension.html">PetscDualSpaceGetDimension</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line119">119: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetInteriorDimension.html">PetscDualSpaceGetInteriorDimension</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line120">120: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetNumComponents.html">PetscDualSpaceSetNumComponents</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line121">121: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetNumComponents.html">PetscDualSpaceGetNumComponents</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line122">122: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetOrder.html">PetscDualSpaceSetOrder</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line123">123: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetOrder.html">PetscDualSpaceGetOrder</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line124">124: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetDM.html">PetscDualSpaceSetDM</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DM/DM.html">DM</a>)</font></strong>;
<a name="line125">125: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetDM.html">PetscDualSpaceGetDM</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DM/DM.html">DM</a> *)</font></strong>;
<a name="line126">126: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetFunctional.html">PetscDualSpaceGetFunctional</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a> *)</font></strong>;
<a name="line127">127: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetSymmetries.html">PetscDualSpaceGetSymmetries</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> ****, const <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> ****)</font></strong>;
<a name="line129">129: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetAllData.html">PetscDualSpaceGetAllData</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a> *, <a href="../manualpages/Mat/Mat.html">Mat</a> *)</font></strong>;
<a name="line130">130: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceCreateAllDataDefault.html">PetscDualSpaceCreateAllDataDefault</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a> *, <a href="../manualpages/Mat/Mat.html">Mat</a> *)</font></strong>;
<a name="line131">131: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetInteriorData.html">PetscDualSpaceGetInteriorData</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a> *, <a href="../manualpages/Mat/Mat.html">Mat</a> *)</font></strong>;
<a name="line132">132: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceCreateInteriorDataDefault.html">PetscDualSpaceCreateInteriorDataDefault</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a> *, <a href="../manualpages/Mat/Mat.html">Mat</a> *)</font></strong>;
<a name="line133">133: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceEqual.html">PetscDualSpaceEqual</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line135">135: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceApplyAll.html">PetscDualSpaceApplyAll</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *, <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *)</font></strong>;
<a name="line136">136: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceApplyAllDefault.html">PetscDualSpaceApplyAllDefault</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *, <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *)</font></strong>;
<a name="line137">137: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceApplyInterior.html">PetscDualSpaceApplyInterior</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *, <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *)</font></strong>;
<a name="line138">138: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceApplyInteriorDefault.html">PetscDualSpaceApplyInteriorDefault</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *, <a href="../manualpages/Sys/PetscScalar.html">PetscScalar</a> *)</font></strong>;
<a name="line140">140: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetFormDegree.html">PetscDualSpaceGetFormDegree</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line141">141: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSetFormDegree.html">PetscDualSpaceSetFormDegree</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line142">142: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetDeRahm.html">PetscDualSpaceGetDeRahm</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line144">144: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetContinuity.html">PetscDualSpaceLagrangeGetContinuity</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line145">145: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetContinuity.html">PetscDualSpaceLagrangeSetContinuity</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line146">146: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetTensor.html">PetscDualSpaceLagrangeGetTensor</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line147">147: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetTensor.html">PetscDualSpaceLagrangeSetTensor</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line148">148: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetTrimmed.html">PetscDualSpaceLagrangeGetTrimmed</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line149">149: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetTrimmed.html">PetscDualSpaceLagrangeSetTrimmed</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line150">150: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetNodeType.html">PetscDualSpaceLagrangeGetNodeType</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscDTNodeType.html">PetscDTNodeType</a> *, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a> *)</font></strong>;
<a name="line151">151: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetNodeType.html">PetscDualSpaceLagrangeSetNodeType</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/DT/PetscDTNodeType.html">PetscDTNodeType</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a>)</font></strong>;
<a name="line152">152: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetUseMoments.html">PetscDualSpaceLagrangeGetUseMoments</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line153">153: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetUseMoments.html">PetscDualSpaceLagrangeSetUseMoments</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line154">154: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeGetMomentOrder.html">PetscDualSpaceLagrangeGetMomentOrder</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line155">155: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceLagrangeSetMomentOrder.html">PetscDualSpaceLagrangeSetMomentOrder</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line157">157: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetHeightSubspace.html">PetscDualSpaceGetHeightSubspace</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line158">158: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceGetPointSubspace.html">PetscDualSpaceGetPointSubspace</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line159">159: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSimpleSetDimension.html">PetscDualSpaceSimpleSetDimension</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line160">160: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSimpleSetFunctional.html">PetscDualSpaceSimpleSetFunctional</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DT/PetscQuadrature.html">PetscQuadrature</a>)</font></strong>;
<a name="line162">162: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceRefinedSetCellSpaces.html">PetscDualSpaceRefinedSetCellSpaces</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, const <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>[])</font></strong>;
<a name="line163">163: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/SPACE/PetscSpaceCreateSubspace.html">PetscSpaceCreateSubspace</a>(<a href="../manualpages/SPACE/PetscSpace.html">PetscSpace</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a> *, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a> *, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a> *, <a href="../manualpages/Sys/PetscReal.html">PetscReal</a> *, <a href="../manualpages/Sys/PetscCopyMode.html">PetscCopyMode</a>, <a href="../manualpages/SPACE/PetscSpace.html">PetscSpace</a> *)</font></strong>;
<a name="line165">165: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumSetNumSubspaces.html">PetscDualSpaceSumSetNumSubspaces</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>)</font></strong>;
<a name="line166">166: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumGetNumSubspaces.html">PetscDualSpaceSumGetNumSubspaces</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a> *)</font></strong>;
<a name="line167">167: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumSetSubspace.html">PetscDualSpaceSumSetSubspace</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>)</font></strong>;
<a name="line168">168: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumGetSubspace.html">PetscDualSpaceSumGetSubspace</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
<a name="line169">169: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumSetConcatenate.html">PetscDualSpaceSumSetConcatenate</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line170">170: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumGetConcatenate.html">PetscDualSpaceSumGetConcatenate</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line171">171: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumSetInterleave.html">PetscDualSpaceSumSetInterleave</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>)</font></strong>;
<a name="line172">172: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceSumGetInterleave.html">PetscDualSpaceSumGetInterleave</a>(<a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *, <a href="../manualpages/Sys/PetscBool.html">PetscBool</a> *)</font></strong>;
<a name="line173">173: </a><strong><font color="#4169E1">PETSC_EXTERN <a href="../manualpages/Sys/PetscErrorCode.html">PetscErrorCode</a> <a href="../manualpages/DUALSPACE/PetscDualSpaceCreateSum.html">PetscDualSpaceCreateSum</a>(<a href="../manualpages/Sys/PetscInt.html">PetscInt</a>, const <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a>[], <a href="../manualpages/Sys/PetscBool.html">PetscBool</a>, <a href="../manualpages/DUALSPACE/PetscDualSpace.html">PetscDualSpace</a> *)</font></strong>;
</pre>
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