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* @defgroup Aprx Aprx class
* @brief The APpRoXimation library object.
*/
/**
* @file aprx.h
* @ingroup Aprx
* @brief Class Aprx: the APpRoXimation library object.
* @author Michael Holst
* @note None
* @version $Id: aprx.h,v 1.37 2010/08/12 05:18:21 fetk Exp $
*
* @attention
* @verbatim
*
* MC = < Manifold Code >
* Copyright (C) 1994-- Michael Holst
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* @endverbatim
*/
#ifndef _APRX_H_
#define _APRX_H_
#include <mc/mc_base.h>
#include <mc/gem.h>
#include <mc/bam.h>
#include <mc/whb.h>
#include <mc/re.h>
#include <mc/node.h>
#include <mc/bnode.h>
/**
* @ingroup Aprx
* @brief Class Aprx: Parameters and datatypes Class Aprx: Definition.
* @author Michael Holst
*/
struct sAprx {
/** @brief the memory manager */
Vmem *vmem;
/** @brief did i make vmem or was it inherited */
int iMadeVmem;
/** @brief geometry machine */
Gem *gm;
/** @brief container for user-provided functions */
PDE *pde;
/** @brief ptr to the Vset object for interactions */
Vset *lnkG;
/** @brief ptr to the master elements */
Re *re[MAXV];
/** @brief ptr to the master bump elements */
Re *reB[MAXV];
/** @brief Global Number of 0-simplices (vertices) */
int numV;
/** @brief Global Number of 1-simplices (edges) */
int numE;
/** @brief Global Number of 2-simplices (faces) */
int numF;
/** @brief Global Number of 3-simplices (simplices) */
int numS;
/** @brief Global Vertex-to-Edge map */
int *I_V2E;
/** @brief Global Vertex-to-Face map */
int *I_V2F;
/** @brief Global Vertex-to-Simplex map */
int *I_V2S;
/** @brief Global Edge-to-Face map */
int *I_E2F;
/** @brief Global Edge-to-Simplex map */
int *I_E2S;
/** @brief Global Face-to-Simplex map */
int *I_F2S;
/** @brief complete node information */
Bnode *B;
/** @brief number of dirichlet boundary nodes */
int numBV[MAXV];
/** @brief dirichlet boundary node numbers */
int *ibv[MAXV];
/** @brief dirichlet boundary node values */
double *bv[MAXV];
/** @brief ELEMENT work vectors */
Bvec *wev;
/** @brief current a posteriori global error over mesh */
double gerror;
/** @brief number of blocks */
int numB;
/** @brief block prolongation operator TO this mesh */
Bmat *P;
/** @brief order of approximation */
int order;
};
/**
* @ingroup Aprx
* @brief Declaration of the Aprx class as the Aprx structure
* @author Michael Holst
* @return None
*/
typedef struct sAprx Aprx;
/*
* ***************************************************************************
* Class Aprx: Inlineable methods (aprx.c)
* ***************************************************************************
*/
#if !defined(VINLINE_APRX)
#else /* if defined(VINLINE_APRX) */
#endif /* if !defined(VINLINE_APRX) */
/**
* @ingroup Aprx
* @brief Construct a linear Approximation object.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return Pointer to a newly allocated (empty) linear Approximation object
* @param vmem Memory management object
* @param tgm Geometry manager source
* @param tpde PDE object
*/
VEXTERNC Aprx* Aprx_ctor(Vmem *vmem, Gem *tgm, PDE *tpde);
/**
* @ingroup Aprx
* @brief Approximation object constructor.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return thee Pointer to an Aprx allocated memory location
* @param vmem Memory management object
* @param tgm Geometry manager source
* @param tpde PDE object
* @param order Order of approximation to be constructed
*/
VEXTERNC Aprx* Aprx_ctor2(Vmem *vmem, Gem *tgm, PDE *tpde,int order);
/**
* @ingroup Aprx
* @brief Approximation object destructor.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @param thee Pointer to object to be destroyed
*/
VEXTERNC void Aprx_dtor(Aprx **thee);
/**
* @ingroup Aprx
* @brief Return the number of blocks.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return the number of blocks
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC int Aprx_numB(Aprx *thee);
/**
* @ingroup Aprx
* @brief Return a pointer to the current prolongation matrix.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return a pointer to the current prolongation matrix.
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC Bmat *Aprx_P(Aprx *thee);
/**
* @ingroup Aprx
* @brief Read in the user-specified initial mesh given in the
* "MCSF" or "MCEF" format, and transform into our internal
* datastructures.\n
* Do a little more than a "Gem_read", in that we also
* initialize the extrinsic and intrinsic spatial dimensions
* corresponding to the input mesh, and we also then build the
* reference elements.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)\n
* See the documentation to Gem_read for a description of the
* mesh input data file format.
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param key input format type
* key=0 ==> simplex format
* key=1 ==> edge format
* key=2 ==> simplex-nabor format
* @param sock socket for reading the external mesh data (NULL otherwise)
*/
VEXTERNC int Aprx_read(Aprx *thee, int key, Vio *sock);
/**
* @ingroup Aprx
* @brief Reset all of the datastructures.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC void Aprx_reset(Aprx *thee);
/**
* @ingroup Aprx
* @brief Make node information.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC void Aprx_initNodes(Aprx *thee);
/**
* @ingroup Aprx
* @brief Determine the node types via a single fast traversal of
* the elements by looking at the element faces.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC void Aprx_buildNodes(Aprx *thee);
/**
* @ingroup Aprx
* @brief Evaluate the trace information.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param Wud block NODAL dirichlet work vector
* @param Wui block NODAL interior dirichlet work vector
* @param Wut block NODAL analytical work vector
*/
VEXTERNC void Aprx_evalTrace(Aprx *thee, Bvec *Wud, Bvec *Wui, Bvec *Wut);
/**
* @ingroup Aprx
* @brief Refine the mesh.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param rkey Boolean sets the rkey type for refining the mesh.
* Input: If (rkey==0) Perform recursive simplex bisection until conformity
*
* If (rkey==1) Perform first quadra-[octa-]-section, followed by
* recursive simplex bisection until conformity
*
* IMPORTANT NOTE: In 2D, (rkey==1) WILL generate
* a conforming mesh. However, in 3D, this procedure
* will in general produce nonconforming simplices.
* To produce a conforming mesh in 3D would require an
* implementation covering all possible face refinement
* combinations (something like 169 cases). This has
* been done e.g. by Jurgen Bey in AGM, but we are
* not that patient; use (rkey==0) above if you want
* a conforming mesh...
*
* If (rkey==2) As a test of the conformity procedure, perform
* quadra-[octa-]-section until conformity, which
* should produce a uniformly regularly refined mesh.
* (In 2D, each triangle should be divided into four
* children, and in 3D each tetrahedron should be
* divided into eight children.)
* @param bkey Boolean sets the bkey type for bisecting the mesh
* If (bkey==0) Bisection type: Longest Edge
* If (bkey==1) Bisection type: Newest Vertex
* If (bkey==2) Bisection type: Newest Pair
* @param pkey Boolean sets the pkey type to prolongate a vector
*/
VEXTERNC int Aprx_refine(Aprx *thee, int rkey, int bkey, int pkey);
/**
* @ingroup Aprx
* @brief Unrefine the mesh.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param rkey Boolean sets the rkey type for un-refining the mesh.
* @param pkey Boolean sets the pkey type to prolongate a vector
*/
VEXTERNC int Aprx_unRefine(Aprx *thee, int rkey, int pkey);
/**
* @ingroup Aprx
* @brief Deform the mesh
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return Success enumeration for deforming the mesh.
* @param thee Pointer to an Aprx allocated memory location
* @param def The corresponding deforming block vector
*/
VEXTERNC int Aprx_deform(Aprx *thee, Bvec *def);
/**
* @ingroup Aprx
* @brief Create storage for and build prolongation operator; the operator
* prolongates a vector FROM a coarser level TO this level.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param numRc number of vertices before refinement
* @param numR number of vertices after refinement
* @param pkey Boolean sets the pkey type to prolongate a vector
*/
VEXTERNC void Aprx_buildProlong(Aprx *thee, int numRc, int numR, int pkey);
/**
* @ingroup Aprx
* @brief Create block version of prolongation operator; also
* updates the Bnode object.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param p Pointer to Bnode matrix
*/
VEXTERNC void Aprx_buildProlongBmat(Aprx *thee, Mat *p);
/**
* @ingroup Aprx
* @brief Count up the total number of basis functions (nodes).
* This is basically an a priori count of the number of rows in
* the stiffness matrix.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c) \n
* This routine can handle COMPLETELY GENERAL ELEMENTS; see the
* comments in Aprx_interact().
* @return the total number of basis functions (nodes).
* @param thee Pointer to an Aprx allocated memory location
* @param re a reference simplex element object.
*/
VEXTERNC int Aprx_nodeCount(Aprx *thee, Re *re);
/**
* @ingroup Aprx
* @brief Count the number of basis (linear/quadratic/etc) functions which
* interact with a given basis function. This is basically an
* a priori count of the number of nonzeros per row in the
* stiffness matrix, and the number of nozeros per row above the
* diagonal (and thus the number of nonzeros per column below the
* diagonal if we have symmetric nonzero structure). By doing this
* count, we can one-time malloc storage for matrices before
* assembly, and avoid extra copies as well as avoid the use
* of linked list structures for representing matrices with
* a priori unknown nonzero structure.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)\n
* This routine can handle COMPLETELY GENERAL ELEMENTS; all it needs
* to do is simply compute all interactions of all nodes in the
* element. The nodes may be any combination of vertex-based,
* edge-based, face-based (3D only), or simplex-based (interior)
* degrees of freedom.\n
* This calculation is made possible because all of the node numbers
* for all of the vertex/edge/face/simplex-nodes in each simplex are
* available in O(1) time for each element, using the geometry
* manager routine Gem_simplexInfo().
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param re a reference simplex element object.
* @param reT a reference simplex element object.
* @param numR num of rows in the matrix
* @param numO num of nonzeros we are actually storing in the
* strict upper-triangle of matrix. (DRC only)
* @param numOYR YSMP-row(col)
* @param IJA integer structure [ IA ; JA ]
* @param IJAYR lower-triangle block from upper triangle block
*/
VEXTERNC void Aprx_interact(Aprx *thee, Re *re, Re *reT,
int *numR, int *numO, int *numOYR, int **IJA, int **IJAYR);
/**
* @ingroup Aprx
* @brief Determine all basis function interations.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param re array of reference simplex element objects
* @param reT array of reference simplex element objects
* @param sym symmetry keys for the matrix
* @param mirror block mirror keys for the matrix
* @param frmt Matrix format
* @param numR num of rows in the matrix
* @param numO num of nonzeros we are actually storing in the
* strict upper-triangle of matrix. (DRC only)
* @param IJA integer structure [ IA ; JA ]
*/
VEXTERNC void Aprx_interactBlock(Aprx *thee, Re *re[MAXV], Re *reT[MAXV],
MATsym sym[MAXV][MAXV], MATmirror mirror[MAXV][MAXV], MATformat frmt[MAXV][MAXV],
int numR[MAXV], int numO[MAXV][MAXV], int *IJA[MAXV][MAXV]);
/**
* @ingroup Aprx
* @brief Compute global index of node of dimension dim in the matrix
* @author Michael Holst, Oleg Korobkin
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return global index of node of dimension dim in the matrix
* @param thee Pointer to an Aprx allocated memory location
* @param re Pointer to the reference elemented to be used
* @param i i-simplex global number
* @param dim interactions index
* @param q number of volume quadrature points
*/
VEXTERNC int Aprx_nodeIndex (Aprx *thee, Re *re, int i, int dim, int q);
/**
* @ingroup Aprx
* @brief Given an index of node DF within the simplex and
* its TT structure, compute global index for that node
* @authors Michael Holst and Oleg Korobkin
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return global index for the node by given an index of node DF within
* the simplex
* @param thee Pointer to an Aprx allocated memory location
* @param re Pointer to the reference elemented to be used
* @param t Pointer to class T
* @param idf index of node DF within the simplex
*/
VEXTERNC int Aprx_nodeIndexTT (Aprx *thee, Re *re, TT *t, int idf);
/**
* @ingroup Aprx
* @brief Build boundary Bnode information into two Bmats.
* @authors Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)\n
* Either/both Bmat objects can be VNULL without error;
* the result for that VNULL Bmat is a No-Op.
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param A Pointer to stiffness matrix
* @param M Pointer to Mass matrix
*/
VEXTERNC void Aprx_buildBRC(Aprx *thee, Bmat *A, Bmat *M);
/**
* @ingroup Aprx
* @brief Initialize vector test function "i" and its gradient,
* generated by scalar test function "r" for this element.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (aprx.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param i vector test function index
* @param r scalar test function index
* @param phi values of local basis funcs at integ pt
* @param phix first derivs of local basis funcs at integ pt
* @param V vector test function
* @param dV first derivs of vector test function
*/
VEXTERNC void Aprx_initSpace(Aprx *thee, int i, int r,
double phi[], double phix[][3], double V[], double dV[][3]);
#if 0
/**
* @ingroup Aprx
* @brief Build the scalar basis functions and their gradients
* on this element. Also build an interpolant of the
* solution and its gradient.\n
* evalKey==0 ==> use U=[0+ud] as evaluation point \n
* evalKey>=1 ==> use U=[u+ud] as evaluation point
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (assem.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param re a reference simplex element object.
* @param evalKey evalKey==0 ==> use U=[0+ud] as evaluation point \n
* evalKey>=1 ==> use U=[u+ud] as evaluation point
* @param qp index of quad pts
* @param face index of face types
* @param t pointer to class T
* @param xq coordinates of quad pts
* @param phi values of local basis funcs at integ pt
* @param phix first derivs of local basis funcs at integ pt
* @param U block NODAL solution vector
* @param dU first derivs of block NODAL solution vector
* @param Wu block NODAL solution work vector
* @param Wud block NODAL dirichlet work vector
*/
VEXTERNC void Aprx_buildBasis(Aprx *thee, Re *re,
int evalKey, int qp, int face, TT *t,
double xq[], double phi[], double phix[][3],
double U[], double dU[][3],
Bvec *Wu, Bvec *Wud);
#endif
/**
* @ingroup Aprx
* @brief Initialize an element matrix.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (assem.c)
* @param thee Pointer to an Aprx allocated memory location
* @param bumpKey == 0 ==> Do not assemble with bumps.\n
* == 1 ==> Assemble bilinear form with bumps.\n
* == 2 ==> Assemble residual form with bumps.\n
* == ? ==> Same as 1.\n
* @param t Pointer to class T
* @param em Pointer to element matrix
*/
VEXTERNC void Aprx_initEmat(Aprx *thee, int bumpKey, TT *t, Emat *em);
/**
* @ingroup Aprx
* @brief Build an element matrix and an element load vector for a
* single given element, using quadrature.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (assem.c) \n
* We handle both the volume and surface cases here, using
* "face" and "t" as follows: \n
* face < 0 ==> do volume quadrature; we take the node numbers
* as just the identity mapping.\n
* face >= 0 ==> do face quadrature for face "face", where the node
* numbers for face are taken from t->loc[face][].
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param evalKey == 0 ==> Primal problem: evaluation at z=[0+ud].\n
* == 1 ==> Primal problem: evaluation at z=[u+ud].\n
* == 2 ==> Dual problem: evaluation at z=[0+ud].\n
* == 3 ==> Dual problem: evaluation at z=[u+ud].\n
* == ? ==> Same as 0.
* @param energyKey == 0 ==> DON'T assemble an energy.\n
* == 1 ==> Assemble the energy J(z).\n
* == 2 ==> Assemble the energy 0.\n
* == ? ==> Same as 0.
* @param residKey == 0 ==> DON'T assemble a residual.\n
* == 1 ==> Assemble the residual F(z)(v).\n
* == 2 ==> Assemble the residual 0.\n
* == ? ==> Same as 0.
* @param tangKey == 0 ==> DON'T assemble a tangent matrix.\n
* == 1 ==> Assemble the tangent matrix DF(z)(w,v).\n
* == 2 ==> Assemble the tangent matrix 0.\n
* == ? ==> Same as 0.
* @param massKey == 0 ==> DON'T assemble a mass matrix.\n
* == 1 ==> Assemble the mass matrix p(w,v).\n
* == 2 ==> Assemble the mass matrix 0.\n
* == ? ==> Same as 0.
* @param bumpKey == 0 ==> Do not assemble with bumps.\n
* == 1 ==> Assemble bilinear form with bumps.\n
* == 2 ==> Assemble residual form with bumps.\n
* == ? ==> Same as 1.\n
* @param face face < 0 ==> do volume quadrature; we take the node
* numbers as just the identity mapping.\n
* face >= 0 ==> do face quadrature for face "face", where
* the node numbers for face are taken from t->loc[face][].
* @param t Pointer to class T
* @param em Pointer to element matrix
* @param Wu block NODAL solution work vector
* @param Wud block NODAL dirichlet work vector
*/
VEXTERNC void Aprx_quadEmat(Aprx *thee,
int evalKey, int energyKey, int residKey, int tangKey, int massKey,
int bumpKey,
int face, TT *t, Emat *em,
Bvec *Wu, Bvec *Wud);
/**
* @ingroup Aprx
* @brief Fan out an element matrix to the global matrix,
* and fan out an element vector to the global vector.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (assem.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param evalKey == 0 ==> Primal problem: evaluation at z=[0+ud].\n
* == 1 ==> Primal problem: evaluation at z=[u+ud].\n
* == 2 ==> Dual problem: evaluation at z=[0+ud].\n
* == 3 ==> Dual problem: evaluation at z=[u+ud].\n
* == ? ==> Same as 0.
* @param energyKey == 0 ==> DON'T assemble an energy.\n
* == 1 ==> Assemble the energy J(z).\n
* == 2 ==> Assemble the energy 0.\n
* == ? ==> Same as 0.
* @param residKey == 0 ==> DON'T assemble a residual.\n
* == 1 ==> Assemble the residual F(z)(v).\n
* == 2 ==> Assemble the residual 0.\n
* == ? ==> Same as 0.
* @param tangKey == 0 ==> DON'T assemble a tangent matrix.\n
* == 1 ==> Assemble the tangent matrix DF(z)(w,v).\n
* == 2 ==> Assemble the tangent matrix 0.\n
* == ? ==> Same as 0.
* @param massKey == 0 ==> DON'T assemble a mass matrix.\n
* == 1 ==> Assemble the mass matrix p(w,v).\n
* == 2 ==> Assemble the mass matrix 0.\n
* == ? ==> Same as 0.
* @param bumpKey == 0 ==> Do not assemble with bumps.\n
* == 1 ==> Assemble bilinear form with bumps.\n
* == 2 ==> Assemble residual form with bumps.\n
* == ? ==> Same as 1.\n
* @param em Pointer to element matrix
* @param A Pointer to stiffness matrix
* @param M Pointer to Mass matrix
* @param F Pointer to residual vector
*/
VEXTERNC void Aprx_fanEmat(Aprx *thee,
int evalKey, int energyKey, int residKey, int tangKey, int massKey,
int bumpKey,
Emat *em,
Bmat *A, Bmat *M, Bvec *F);
/**
* @ingroup Aprx
* @brief Assemble one element matrix.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (assem.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param sm Pointer to a given simplex
* @param evalKey == 0 ==> Primal problem: evaluation at z=[0+ud].\n
* == 1 ==> Primal problem: evaluation at z=[u+ud].\n
* == 2 ==> Dual problem: evaluation at z=[0+ud].\n
* == 3 ==> Dual problem: evaluation at z=[u+ud].\n
* == ? ==> Same as 0.
* @param energyKey == 0 ==> DON'T assemble an energy.\n
* == 1 ==> Assemble the energy J(z).\n
* == 2 ==> Assemble the energy 0.\n
* == ? ==> Same as 0.
* @param residKey == 0 ==> DON'T assemble a residual.\n
* == 1 ==> Assemble the residual F(z)(v).\n
* == 2 ==> Assemble the residual 0.\n
* == ? ==> Same as 0.
* @param tangKey == 0 ==> DON'T assemble a tangent matrix.\n
* == 1 ==> Assemble the tangent matrix DF(z)(w,v).\n
* == 2 ==> Assemble the tangent matrix 0.\n
* == ? ==> Same as 0.
* @param massKey == 0 ==> DON'T assemble a mass matrix.\n
* == 1 ==> Assemble the mass matrix p(w,v).\n
* == 2 ==> Assemble the mass matrix 0.\n
* == ? ==> Same as 0.
* @param bumpKey == 0 ==> Do not assemble with bumps.\n
* == 1 ==> Assemble bilinear form with bumps.\n
* == 2 ==> Assemble residual form with bumps.\n
* == ? ==> Same as 1.\n
* @param em Pointer to element matrix
* @param Wu block NODAL solution work vector
* @param Wud block NODAL dirichlet work vector
*/
VEXTERNC void Aprx_assemEmat(Aprx *thee, SS *sm,
int evalKey, int energyKey, int residKey, int tangKey, int massKey,
int bumpKey,
Emat *em,
Bvec *Wu, Bvec *Wud);
/**
* @ingroup Aprx
* @brief Assemble the tangent matrix and nonlinear residual
* vector (which reduces to the normal stiffness matrix and load
* vector in the case of a linear problem) for a general nonlinear
* system of m components in spatial dimension d.
* @note Class Aprx: Non-inlineable methods (assem.c) \n
* The nonlinear residual should always be ZERO at dirichlet nodes!
* @author Michael Holst
* @return the assembled energy
* @param thee Pointer to an Aprx allocated memory location
* @param evalKey == 0 ==> Primal problem: evaluation at z=[0+ud].\n
* == 1 ==> Primal problem: evaluation at z=[u+ud].\n
* == 2 ==> Dual problem: evaluation at z=[0+ud].\n
* == 3 ==> Dual problem: evaluation at z=[u+ud].\n
* == ? ==> Same as 0.
* @param energyKey == 0 ==> DON'T assemble an energy.\n
* == 1 ==> Assemble the energy J(z).\n
* == 2 ==> Assemble the energy 0.\n
* == ? ==> Same as 0.
* @param residKey == 0 ==> DON'T assemble a residual.\n
* == 1 ==> Assemble the residual F(z)(v).\n
* == 2 ==> Assemble the residual 0.\n
* == ? ==> Same as 0.
* @param tangKey == 0 ==> DON'T assemble a tangent matrix.\n
* == 1 ==> Assemble the tangent matrix DF(z)(w,v).\n
* == 2 ==> Assemble the tangent matrix 0.\n
* == ? ==> Same as 0.
* @param massKey == 0 ==> DON'T assemble a mass matrix.\n
* == 1 ==> Assemble the mass matrix p(w,v).\n
* == 2 ==> Assemble the mass matrix 0.\n
* == ? ==> Same as 0.
* @param bumpKey == 0 ==> Do not assemble with bumps.\n
* == 1 ==> Assemble bilinear form with bumps.\n
* == 2 ==> Assemble residual form with bumps.\n
* == ? ==> Same as 1.\n
* @param ip index for assembled energies
* @param rp parameter for initially assembled PDE
* @param A Pointer to stiffness matrix
* @param M Pointer to Mass matrix
* @param F block NODAL residual vector
* @param Wu block NODAL solution work vector
* @param Wud block NODAL dirichlet work vector
*/
VEXTERNC double Aprx_assem(Aprx *thee,
int evalKey, int energyKey, int residKey, int tangKey, int massKey,
int bumpKey,
int ip[], double rp[],
Bmat *A, Bmat *M, Bvec *F, Bvec *Wu, Bvec *Wud);
/**
* @ingroup Aprx
* @brief Mark simplices to be refined
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (estim.c)\n
* If ( (key == -1) || (key == 0) || (key == 1)) ==>\n
* Let geometry manager deal with it.\n
* If (key == 2) ==> Nonlinear residual indicator.\n
* If (key == 3) ==> Dual-weighted residual indicator.\n
* If (key == 4) ==> Local problem indicator.
* @return number of marked simplices
* @param thee Pointer to an Aprx allocated memory location
* @param key If ( (key == -1) || (key == 0) || (key == 1)) ==>\n
* Let geometry manager deal with it.\n
* If (key == 2) ==> Nonlinear residual indicator.\n
* If (key == 3) ==> Dual-weighted residual indicator.\n
* If (key == 4) ==> Local problem indicator.
* @param color chart type of marked simplices
* @param bkey Bisection type
* @param elevel level to determine the fraction of simplices
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param f block NODAL residual vector
* @param r block NODAL temporary vector
*/
VEXTERNC int Aprx_markRefine(Aprx *thee, int key, int color,
int bkey, double elevel, Bvec *u, Bvec *ud, Bvec *f, Bvec *r);
/**
* @ingroup Aprx
* @brief A posteriori error estimation via several different approaches.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (estim.c)
* @verbatim
Apply one of several a posteriori error estimators:
If (key == 2) ==> Nonlinear residual indicator.
If (key == 3) ==> Dual-weighted residual indicator.
If (key == 4) ==> Local problem indicator.
If (key == 5) ==> Recovered gradient indicator.
The error tolerance can be used in several ways:
If (bkey == 0) ==> mark if: [error/S] > TOL
If (bkey == 1) ==> mark if: [error/S] > (TOL^2/numS)^{1/2}
If (bkey == 2) ==> mark fixed number/fraction (dep. on ETOL):
if elevel < 1, mark fraction of simplices
if elevel >=1, mark that many simplices (rounded to
the smaller integer)
@endverbatim
* @return number of marked simplices
* @param thee Pointer to an Aprx allocated memory location
* @param key index of different types of a posteriori error estimators
* @param color chart type of marked simplices
* @param bkey Bisection type
* @param elevel level to determine the fraction of simplices
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param f block NODAL residual vector
* @param r block NODAL temporary vector
*/
VEXTERNC int Aprx_estRefine(Aprx *thee, int key, int color,
int bkey, double elevel, Bvec *u, Bvec *ud, Bvec *f, Bvec *r);
/**
* @ingroup Aprx
* @brief Selects a fixed number/fraction of simplicies to be refined.
* @author Olen Korobkin, Michael Holst
* @note Class Aprx: Non-inlineable methods (estim.c)
* @verbatim
This function is called by Aprx_markRefine if fixed number /
fraction of simplices <ilevel> has to be refined. Returns
number of marked elements.
@endverbatim
* @return Number of marked elements
* @param thee Pointer to an Aprx allocated memory location
* @param num2ref index for the refined simplex
* @param color chart type of marked simplices
*/
VEXTERNC int Aprx_markRefineFixed (Aprx *thee, int num2ref, int color);
/**
* @ingroup Aprx
* @brief Selects a fixed number/fraction of simplicies to be refined.
* @author Olen Korobkin, Michael Holst
* @note Class Aprx: Non-inlineable methods (estim.c)
* @verbatim
This function is called by Aprx_markRefine. Returns
number of marked elements.
@endverbatim
* @return Number of marked elements
* @param thee Pointer to an Aprx allocated memory location
* @param percentToRefine Percentage to refine
* @param color chart type of marked simplices
*/
VEXTERNC int Aprx_markRefineDorfler (Aprx *thee, double percentToRefine, int color);
/**
* @ingroup Aprx
* @brief Evaluate a finite element solution at a set of arbitrary points.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (eval.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param u solution vector
* @param block index for the block
* @param numPts number of all interpolation pts for one simplex
* @param pts coordinates of the pt
* @param vals solution for the interpolated pts
* @param marks index for marked or not
*/
VEXTERNC void Aprx_evalFunc(Aprx *thee,
Bvec *u, int block, int numPts, double *pts,
double *vals, int *marks);
/**
* @ingroup Aprx
* @brief Interpolates data onto finite difference grid
* @author Michael Holst, Doug Arnold and Karen Camarda
* @note Class Aprx: Non-inlineable methods (eval.c)\n
* Much is lifted from Aprx_evalFunc,
* with some ideas from Doug Arnold.
* Contributed by Karen Camarda.
* @verbatim
* Example: Below is a matlab example courtesy of Doug Arnold.
*
* %-- BEGIN MATLAB CODE --------------------------------------------------
*
* function colormesh
*
* % This file demonstrates how to go from an unstructured grid to
* % a structured one. Each point on the structured grid is colored
* % according to which triangle in the unstructured grid it belongs to.
*
* % Douglas N. Arnold, 3/4/98
*
* % set up a mesh
* npts=10;
* x=[ 1.13 1.66 0.50 0.46 0.26 0.20 0.70 1.93 1.01 0.65 ];
* y=[ 1.81 1.23 0.99 1.30 1.29 1.50 1.10 0.68 0.60 0.07 ];
* tri = delaunay(x,y);
* ntri=size(tri,1);
*
* % grid spacing
* h=.03;
* k=.04;
*
* clf
* [z,i]=sort(rand(64,1));
* colormap hsv;
* cmap = colormap;
* cmap=cmap(i,:,:);
*
* % loop over triangles
* for m = 1:ntri
* % get vertices of triangle i
* v1=[x(tri(m,1)),y(tri(m,1))];
* v2=[x(tri(m,2)),y(tri(m,2))];
* v3=[x(tri(m,3)),y(tri(m,3))];
*
* % plot the triangle
* ttt=[v1;v2;v3;v1];
* line(ttt(:,1),ttt(:,2),'color','green')
*
* % find bounding box of triangle
* xmin = min([v1(1),v2(1),v3(1)]);
* xmax = max([v1(1),v2(1),v3(1)]);
* ymin = min([v1(2),v2(2),v3(2)]);
* ymax = max([v1(2),v2(2),v3(2)]);
*
* % loop through grid points in bounding box, plotting those in triangle
* for i = ceil(xmin/h):floor(xmax/h)
* for j = ceil(ymin/k):floor(ymax/k)
* if intriangle(v1,v2,v3,[i*h,j*k])
* % set color according to triangle number
* color = cmap(m,:);
* line(i*h,j*k,'marker','.','markersize',10,'color',color)
* end
* end
* end
*
* end
*
* function i = intriangle(v1,v2,v3,x)
* % INTRIANGLE -- check if a point belongs to a triangle
* %
* % f = intriangle(v1,v2,v3,x)
* %
* % input:
* % v1,v2,v3 2-vectors giving the vertices of the triangle
* % x 2-vector giving the point
* %
* % output:
* % i 1 if x belongs to the close triangle, 0 else
*
* % map point under affine mapping from given triangle to ref triangle
* xhat = (x-v1)/[v2-v1;v3-v1];
* % check if mapped point belongs to reference triangle
* i = xhat(1) >= 0 & xhat(2) >= 0 & 1-xhat(1)-xhat(2) >= 0;
* %-- END MATLAB CODE --------------------------------------------------
*
* ***************************************************************************
@endverbatim
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param u solution vector
* @param block index of block
* @param nx number of grids in X coordinates
* @param ny number of grids in y coordinates
* @param nz number of grids in z coordinates
* @param x0 x coordinate of lower grid corner
* @param y0 y coordinate of lower grid corner
* @param z0 z coordinate of lower grid corner
* @param dx Grid spacing in x direction
* @param dy Grid spacing in y direction
* @param dz Grid spacing in z direction
* @param derivs index for different nfunc types
* @param outTypeKey ASCII output or Binary output
*/
VEXTERNC void Aprx_fe2fd(Aprx *thee, Bvec *u, int block,
int nx, int ny, int nz,
double x0, double y0, double z0, double dx, double dy, double dz,
int derivs, int outTypeKey);
/**
* @ingroup Aprx
* @brief Evaluate a given boundary integral.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (eval.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param ut block NODAL analytical vector
*/
VEXTERNC void Aprx_bndIntegral(Aprx *thee, Bvec *u, Bvec *ud, Bvec *ut);
/**
* @ingroup Aprx
* @brief Evaluate ADM mass from conformal factor.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (eval.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param ut block NODAL analytical vector
* @param block index of a block
*/
VEXTERNC void Aprx_admMass(Aprx *thee, Bvec *u, Bvec *ud, Bvec *ut, int block);
/**
* @ingroup Aprx
* @brief Evaluate error in solution in one of several norms.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (eval.c) \n
* We evaluate the error in the solution (in the case that
* an exact analytical solution is available) in one of several
* norms:\n
* If (key == 0) ==> L^2 norm of the error.\n
* If (key == 1) ==> L^{\\infty} norm of the error.\n
* If (key == 2) ==> H^1 norm of the error.
* @return error in solution in one of several norms.
* @param thee Pointer to an Aprx allocated memory location
* @param pcolor simplex chart type
* @param key If (key == 0) ==> L^2 norm of the error.\n
* If (key == 1) ==> L^{\\infty} norm of the error.\n
* If (key == 2) ==> H^1 norm of the error.
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param ut block NODAL analytical vector
*/
VEXTERNC double Aprx_evalError(Aprx *thee, int pcolor, int key,
Bvec *u, Bvec *ud, Bvec *ut);
/**
* @ingroup Aprx
* @brief Evaluate difference of two functions in H1 norm in one element.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (eval.c) \n
* We evaluate difference of two functions in H1 norm in one element.
* @return Difference of two functions in H1 norm in one element.
* @param thee Pointer to an Aprx allocated memory location
* @param sm simplex
* @param u block NODAL solution vector
* @param ud block NODAL dirichlet vector
* @param ut block NODAL analytical vector
*/
VEXTERNC double Aprx_evalH1(Aprx *thee, SS *sm, Bvec *u, Bvec *ud, Bvec *ut);
/**
* @ingroup Aprx
* @brief Write a finite element mesh or mesh function in some format.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (io.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param sock socket for reading the external mesh data (NULL otherwise)
* @param defKey defKey == 0 ==> draw mesh as it is
* defKey == 1 ==> use "def??" as new vertex coords (deformation)
* defKey == 2 ==> add "def??" to old vertex coords (displacement)
*
* @param colKey colKey == 0 ==> color simplices all same default color
* colKey == 1 ==> color simplices based on their chart
* colKey == 2 ==> color boundary simplices based on type
*
* @param chartKey chartKey < 0 ==> draw all simplices
* chartKey >= 0 ==> draw only simplices with chart chartKey
*
* @param gluVal gluVal == 1. ==> draw all simplices glued together
* 0. < gluVal < 1. ==> draw simplices with some separation
*
* @param fkey fkey == 0 ==> draw simplices
* fkey == 1 ==> draw only simplex boundary faces
* fkey == 2 ==> draw only simplices with a boundary face
* @param u block NODAL solution vector
* @param format GV/MATH format
*/
VEXTERNC void Aprx_writeGEOM(Aprx *thee, Vio *sock,
int defKey, int colKey, int chartKey, double gluVal, int fkey,
Bvec *u, char *format);
/**
* @ingroup Aprx
* @brief Write a finite element mesh or mesh function in some format.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (io.c)
* @return None
* @param thee Pointer to an Aprx allocated memory location
* @param sock socket for reading the external mesh data (NULL otherwise)
* @param u block NODAL solution vector
* @param format GV/MATH format
*/
VEXTERNC void Aprx_writeSOL(Aprx *thee, Vio *sock, Bvec *u, char *format);
/**
* @ingroup Aprx
* @brief Clear the partitioning (set all colors to pcolor).
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param pcolor simplex chart type
*/
VEXTERNC int Aprx_partSet(Aprx *thee, int pcolor);
/**
* @ingroup Aprx
* @brief Smooth the partitioning.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)
* @return counted number of partitions
* @param thee Pointer to an Aprx allocated memory location
*/
VEXTERNC int Aprx_partSmooth(Aprx *thee);
/**
* @ingroup Aprx
* @brief Partition the domain using inertial bisection.
* Partition sets of points in R^d (d=2 or d=3) by viewing them
* as point masses of a rigid body, and by then employing the
* classical mechanics ideas of inertia and Euler axes.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)\n
* We first locate the center of mass, then change the coordinate
* system so that the center of mass is located at the origin.
* We then form the (symmetric) dxd inertia tensor, and then find
* the set of (real) eigenvalues and (orthogonal) eigenvectors.
* The eigenvectors represent the principle inertial rotation axes,
* and the eigenvalues represent the inertial strength in those
* principle directions. The smallest inerial component along an
* axis represents a direction along which the rigid body is most
* "line-like" (assuming all the points have the same mass). \n
* For our purposes, it makes sense to using the axis (eigenvector)
* corresponding to the smallest inertia (eigenvalue) as the line to
* bisect with a line (d=2) or a plane (d=3). We know the center of
* mass, and once we also have this particular eigenvector, we can
* effectively bisect the point set into the two regions separated
* by the line/plane simply by taking an inner-product of the
* eigenvector with each point (or rather the 2- or 3-vector
* representing the point). A positive inner-product represents one
* side of the cutting line/plane, and a negative inner-product
* represents the other side (a zero inner-product is right on the
* cutting line/plane, so we arbitrarily assign it to one region or
* the other).
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param pcolor simplex chart type
* @param numC number of columns in the matrix
* @param evec eigenvector
* @param simH simHelper class
*/
VEXTERNC int Aprx_partInert(Aprx *thee, int pcolor,
int numC, double *evec, simHelper *simH);
/**
* @ingroup Aprx
* @brief Partition the domain using spectral bisection.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)\n
* @verbatim
* We solve the following generalized eigenvalue problem:
*
* Ax = lambda Bx
*
* for second smallest eigenpair. We then return the eigenvector
* from the pair. We make this happen by turning it into a
* regular eigenvalue problem:
*
* B^{-1/2} A B^{-1/2} ( B^{1/2} x ) = lambda ( B^{1/2} x )
*
* or rather
*
* C y = lambda y, where C=B^{-1/2}AB^{-1/2}, y=B^{1/2}x.
*
* The matrix "B" is simply a diagonal matrix with a (positive)
* error estimate for the element on the diagonal. Therefore, the
* matrix B^{-1/2} is a well-defined positive diagonal matrix.
*
* We explicitly form the matrix C and then send it to the inverse
* Rayleigh-quotient iteration to recover the second smallest
* eigenpair. On return, we scale the eigenvector y by B^{-1/2} to
* recover the actual eigenvector x = B^{-1/2} y.
*
* To handle the possibility that an element has zero error, in
* which case the B matrix had a zero on the diagonal, we set the
* corresponding entry in B^{-1/2} to be 1.
* @endverbatim
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param pcolor simplex chart type
* @param numC number of columns in the matrix
* @param evec eigenvector
* @param simH simHelper class
* @param ford temporary storage ford array
* @param rord temporary storage rord array
* @param general index for creating different scaling matrix
*/
VEXTERNC int Aprx_partSpect(Aprx *thee, int pcolor,
int numC, double *evec, simHelper *simH, int *ford, int *rord,
int general);
/**
* @ingroup Aprx
* @brief Do recursive bisection.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)
* @return Success enumeration
* @param thee Pointer to an Aprx allocated memory location
* @param pkey index for different partition option
* @param pwht index for weighted partitioning
* @param ppow partitioning steps
*/
VEXTERNC int Aprx_part(Aprx *thee, int pkey, int pwht, int ppow);
/**
* @ingroup Aprx
* @brief Do a single bisection step.
* @author Michael Holst
* @note Class Aprx: Non-inlineable methods (parti.c)
* @param thee Pointer to an Aprx allocated memory location
* @param pkey partition method
* @param pwht partitioning weighting
* @param pcolor simplex chart type
* @param poff an index
*/
VEXTERNC int Aprx_partOne(Aprx *thee, int pkey, int pwht, int pcolor, int poff);
#endif /* _APRX_H_ */
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