AM class

A multilevel finite element algebra object. More...


Files

file  am.h
 Class AM: a multilevel finite element algebra object.

Classes

struct  sAM
 Class AM: Definition. More...

Typedefs

typedef struct sAM AM
 Declaraction of the AM class as the AM structure.

Functions

void AM_tSolve (AM *thee, int meth, double dt, double t0, int numstep, int pfreq, int efreq, int ekeytotal, DYNtype pdetype, double ltol, int lmax, SVio *vsock)
 Solution of Time-Dependent problems by Method of Lines.
AM * AM_ctor (Vmem *vmem, Aprx *taprx)
 The AM constructor.
void AM_dtor (AM **thee)
 The AM destructor.
void AM_create (AM *thee)
 Create the following internal Alg structures:
A ==> The tangent matrix (linearization operator)
M ==> The mass matrix
W[] ==> The node vectors.
void AM_destroy (AM *thee)
 Destroy the following internal Alg structures:
A ==> The tangent matrix (linearization operator)
M ==> The mass matrix
W[] ==> The node vectors.
int AM_markRefine (AM *thee, int key, int color, int bkey, double elevel)
 Mark a given mesh for refinement.
int AM_refine (AM *thee, int rkey, int bkey, int pkey)
 Refine the mesh.
int AM_unRefine (AM *thee, int rkey, int pkey)
 Un-refine the mesh.
int AM_deform (AM *thee)
 Deform the mesh.
int AM_read (AM *thee, int key, Vio *sock)
 Read in the user-specified initial mesh given in the "MCSF" or "MCEF" format, and transform into our internal datastructures.
Do a little more than a "Aprx_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.
double AM_assem (AM *thee, int evalKey, int energyKey, int residKey, int tangKey, int massKey, int bumpKey, Bvec *u, Bvec *ud, Bvec *f, int ip[], double rp[])
 Assemble the linearized problem at a given level.
double AM_evalJ (AM *thee)
 Assemble the energy functional at the current solution.
void AM_evalFunc (AM *thee, int number, int block, int numPts, double *pts, double *vals, int *marks)
 Evaluate a finite element function.
void AM_bndIntegral (AM *thee)
 Perform a boundary integral.
double AM_evalError (AM *thee, int pcolor, int key)
 Evaluate error in the current solution.
void AM_applyDiriZero (AM *thee, Bvec *which)
 Apply zero dirichlet condition at a given level.
void AM_iniGuess (AM *thee, Bvec *which)
 Setup an initial guess at a given level.
int AM_part (AM *thee, int pkey, int pwht, int ppow)
 Partition the mesh using the matching Alg level.
int AM_partSet (AM *thee, int pcolor)
 Set the partition color.
int AM_partSmooth (AM *thee)
 Do a partition smoothing.
void AM_printJ (AM *thee)
 Print the energy.
void AM_printA (AM *thee)
 Print the system matrix.
void AM_printAnoD (AM *thee)
 Print the system matrix with Dirichlet rows/cols zeroed.
void AM_printAsp (AM *thee, char *fname)
 Print the system matrix in MATLAB sparse format.
void AM_printAspNoD (AM *thee, char *fname)
 Print the system matrix in MATLAB sparse format with Dirichlet rows/cols zeroed.
void AM_printP (AM *thee)
 Print the prolongation matrix.
void AM_printPsp (AM *thee, char *fname)
 Print the prolongation matrix in MATLAB sparse format.
void AM_printV (AM *thee, int num)
 Print a specified vector.
void AM_printVsp (AM *thee, int num, char *fname)
 Print a vector in MATLAB sparse format.
void AM_writeGEOM (AM *thee, Vio *sock, int defKey, int colKey, int chartKey, double gluVal, int fkey, int number, char *format)
 Write out a mesh in some format.
void AM_writeSOL (AM *thee, Vio *sock, int number, char *format)
 Write out a solution in some format.
void AM_memChk (AM *thee)
 Print the exact current malloc usage.
void AM_lSolve (AM *thee, int prob, int meth, int itmax, double etol, int prec, int gues, int pjac)
 Linear solver.
void AM_hlSolve (AM *thee, int prob, int meth, int itmax, double etol, int prec, int gues, int pjac)
 Hierarchical linear solver.
void AM_nSolve (AM *thee, int meth, int itmax, double etol, int lmeth, int litmax, double letol, int lprec, int gues, int pjac)
void AM_newton (AM *thee, int itmax, double etol, int lmeth, int litmax, double letol, int lprec, int pjac, double loadParm)
 Damped-Inexact Newton iteration.
VPUBLIC void AM_homotopy (AM *thee, int itmax, double etol, int lmeth, int litmax, double letol, int lprec, int pjac)
 Homotopy and the related "incremental loading" iterations.

Detailed Description

A multilevel finite element algebra object.

Typedef Documentation

typedef struct sAM AM

Declaraction of the AM class as the AM structure.

Author:
Michael Holst

Function Documentation

void AM_applyDiriZero ( AM *  thee,
Bvec *  which 
)

Apply zero dirichlet condition at a given level.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
which the block vector

double AM_assem ( AM *  thee,
int  evalKey,
int  energyKey,
int  residKey,
int  tangKey,
int  massKey,
int  bumpKey,
Bvec *  u,
Bvec *  ud,
Bvec *  f,
int  ip[],
double  rp[] 
)

Assemble the linearized problem at a given level.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
the assembled energy
Parameters:
thee Pointer to class AM
evalKey == 0 ==> Primal problem: evaluation at z=[0+ud].
== 1 ==> Primal problem: evaluation at z=[u+ud].
== 2 ==> Dual problem: evaluation at z=[0+ud].
== 3 ==> Dual problem: evaluation at z=[u+ud].
== ? ==> Same as 0.
energyKey == 0 ==> DON'T assemble an energy.
== 1 ==> Assemble the energy J(z).
== 2 ==> Assemble the energy 0.
== ? ==> Same as 0.
residKey == 0 ==> DON'T assemble a residual.
== 1 ==> Assemble the residual F(z)(v).
== 2 ==> Assemble the residual 0.
== ? ==> Same as 0.
tangKey == 0 ==> DON'T assemble a tangent matrix.
== 1 ==> Assemble the tangent matrix DF(z)(w,v).
== 2 ==> Assemble the tangent matrix 0.
== ? ==> Same as 0.
massKey == 0 ==> DON'T assemble a mass matrix.
== 1 ==> Assemble the mass matrix p(w,v).
== 2 ==> Assemble the mass matrix 0.
== ? ==> Same as 0.
bumpKey == 0 ==> Do not assemble with bumps.
== 1 ==> Assemble bilinear form with bumps.
== 2 ==> Assemble residual form with bumps.
== ? ==> Same as 1.
u block NODAL solution vector
ud block NODAL dirichlet vector
f block NODAL residual vector
ip index for assembled energies
rp parameter for initially assembled PDE

void AM_bndIntegral ( AM *  thee  ) 

Perform a boundary integral.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_create ( AM *  thee  ) 

Create the following internal Alg structures:
A ==> The tangent matrix (linearization operator)
M ==> The mass matrix
W[] ==> The node vectors.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

AM* AM_ctor ( Vmem *  vmem,
Aprx *  taprx 
)

The AM constructor.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Pointer to a newly allocated (empty) AM class
Parameters:
vmem Memory management object
taprx Pointer to linear Approximation object

int AM_deform ( AM *  thee  ) 

Deform the mesh.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Success enumeration for deforming the mesh.
Parameters:
thee Pointer to class AM

void AM_destroy ( AM *  thee  ) 

Destroy the following internal Alg structures:
A ==> The tangent matrix (linearization operator)
M ==> The mass matrix
W[] ==> The node vectors.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_dtor ( AM **  thee  ) 

The AM destructor.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

double AM_evalError ( AM *  thee,
int  pcolor,
int  key 
)

Evaluate error in the current solution.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
error in solution in one of several norms.
Parameters:
thee Pointer to class AM
pcolor simplex chart type
key If (key == 0) ==> L^2 norm of the error.
If (key == 1) ==> L^{\infty} norm of the error.
If (key == 2) ==> H^1 norm of the error.

void AM_evalFunc ( AM *  thee,
int  number,
int  block,
int  numPts,
double *  pts,
double *  vals,
int *  marks 
)

Evaluate a finite element function.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
number the value of variable in the environment as an integer
block index for the block
numPts number of all interpolation pts for one simplex
pts coordinates of the pt
vals solution for the interpolated pts
marks index for marked or not

double AM_evalJ ( AM *  thee  ) 

Assemble the energy functional at the current solution.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
the assembled energy
Parameters:
thee Pointer to Class AM

void AM_hlSolve ( AM *  thee,
int  prob,
int  meth,
int  itmax,
double  etol,
int  prec,
int  gues,
int  pjac 
)

Hierarchical linear solver.

Authors:
Burak Aksoylu, Stephen Bond, and Michael Holst
Note:
Class AM: Non-inlineable methods (lsolv.c)
Returns:
None
Parameters:
thee Pointer to class AM
prob index for primal or dual problem
meth method choice (0=slu,1=mg,2=cg,3=bcg,4=pcg,5=pbcg)
itmax number of iterations to do (the maximum allowed)
etol error tolerance (currently ignored)
prec index for different preconditioners
gues index for initial guess
pjac index for printing the system matrix

VPUBLIC void AM_homotopy ( AM *  thee,
int  itmax,
double  etol,
int  lmeth,
int  litmax,
double  letol,
int  lprec,
int  pjac 
)

Homotopy and the related "incremental loading" iterations.

Authors:
Michael Holst
Note:
Class AM: Non-inlineable methods (nsolv.c)
Returns:
None
Parameters:
thee Pointer to class AM
itmax number of iterations to do (the maximum allowed)
etol error tolerance (currently ignored)
lmeth index for specified linear solver
litmax iteration max for linear solver
letol error tolerance for linear solver
lprec preconditioner for linear solver
pjac index for printing the system matrix

void AM_iniGuess ( AM *  thee,
Bvec *  which 
)

Setup an initial guess at a given level.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
which the block vector

void AM_lSolve ( AM *  thee,
int  prob,
int  meth,
int  itmax,
double  etol,
int  prec,
int  gues,
int  pjac 
)

Linear solver.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (lsolv.c)
Returns:
None
Parameters:
thee Pointer to class AM
prob index for primal or dual problem
meth method choice (0=slu,1=mg,2=cg,3=bcg,4=pcg,5=pbcg)
itmax number of iterations to do (the maximum allowed)
etol error tolerance (currently ignored)
prec index for different preconditioners
gues index for initial guess
pjac index for printing the system matrix

int AM_markRefine ( AM *  thee,
int  key,
int  color,
int  bkey,
double  elevel 
)

Mark a given mesh for refinement.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
number of marked simplices
Parameters:
thee Pointer to class AM
key index of different types of a posteriori error estimators
color chart type of marked simplices
bkey Bisection type
elevel level to determine the fraction of simplices

void AM_memChk ( AM *  thee  ) 

Print the exact current malloc usage.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_newton ( AM *  thee,
int  itmax,
double  etol,
int  lmeth,
int  litmax,
double  letol,
int  lprec,
int  pjac,
double  loadParm 
)

Damped-Inexact Newton iteration.

Authors:
Michael Holst
Note:
Class AM: Non-inlineable methods (nsolv.c)
Returns:
None
Parameters:
thee Pointer to class AM
itmax number of iterations to do (the maximum allowed)
etol error tolerance (currently ignored)
lmeth index for specified linear solver
litmax iteration max for linear solver
letol error tolerance for linear solver
lprec preconditioner for linear solver
pjac index for printing the system matrix
loadParm the incoming load parameter

void AM_nSolve ( AM *  thee,
int  meth,
int  itmax,
double  etol,
int  lmeth,
int  litmax,
double  letol,
int  lprec,
int  gues,
int  pjac 
)

Authors:
Note:
Class AM: Non-inlineable methods (nsolv.c)
Returns:
None
Parameters:
thee Pointer to class AM
meth method choice (0=slu,1=mg,2=cg,3=bcg,4=pcg,5=pbcg)
itmax number of iterations to do (the maximum allowed)
etol error tolerance (currently ignored)
lmeth index for specified linear solver
litmax iteration max for linear solver
letol error tolerance for linear solver
lprec preconditioner for linear solver
gues index for initial guess
pjac index for printing the system matrix

int AM_part ( AM *  thee,
int  pkey,
int  pwht,
int  ppow 
)

Partition the mesh using the matching Alg level.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Success enumeration
Parameters:
thee Pointer to Class AM
pkey index for different partition option
pwht index for weighted partitioning
ppow partitioning steps

int AM_partSet ( AM *  thee,
int  pcolor 
)

Set the partition color.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Success enumeration
Parameters:
thee Pointer to class AM
pcolor simplex chart type

int AM_partSmooth ( AM *  thee  ) 

Do a partition smoothing.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
counted number of partitions
Parameters:
thee Pointer to Class AM

void AM_printA ( AM *  thee  ) 

Print the system matrix.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_printAnoD ( AM *  thee  ) 

Print the system matrix with Dirichlet rows/cols zeroed.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_printAsp ( AM *  thee,
char *  fname 
)

Print the system matrix in MATLAB sparse format.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
fname the system matrix file name

void AM_printAspNoD ( AM *  thee,
char *  fname 
)

Print the system matrix in MATLAB sparse format with Dirichlet rows/cols zeroed.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
fname the system matrix file name

void AM_printJ ( AM *  thee  ) 

Print the energy.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM

void AM_printP ( AM *  thee  ) 

Print the prolongation matrix.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM

void AM_printPsp ( AM *  thee,
char *  fname 
)

Print the prolongation matrix in MATLAB sparse format.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
fname the system matrix file name

void AM_printV ( AM *  thee,
int  num 
)

Print a specified vector.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to Class AM
num the number of block work vector

void AM_printVsp ( AM *  thee,
int  num,
char *  fname 
)

Print a vector in MATLAB sparse format.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
num the number of block work vector
fname the output file name

int AM_read ( AM *  thee,
int  key,
Vio *  sock 
)

Read in the user-specified initial mesh given in the "MCSF" or "MCEF" format, and transform into our internal datastructures.
Do a little more than a "Aprx_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 AM: Non-inlineable methods (am.c)
See the documentation to Aprx_read for a description of the mesh input data file format.
Returns:
Success enumeration
Parameters:
thee Pointer to class AM
key input format type key=0 ==> simplex format key=1 ==> edge format key=2 ==> simplex-nabor format
sock socket for reading the external mesh data (NULL otherwise)

int AM_refine ( AM *  thee,
int  rkey,
int  bkey,
int  pkey 
)

Refine the mesh.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Success enumeration
Parameters:
thee Pointer to class AM
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.)

Parameters:
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
pkey Boolean sets the pkey type to prolongate a vector

void AM_tSolve ( AM *  thee,
int  meth,
double  dt,
double  t0,
int  numstep,
int  pfreq,
int  efreq,
int  ekeytotal,
DYNtype  pdetype,
double  ltol,
int  lmax,
SVio *  vsock 
)

Solution of Time-Dependent problems by Method of Lines.

Authors:
Stephen Bond and Kaihsu Tai
Note:
Class Dyn: Non-Inlineable methods (dyn.c)
Returns:
None
Parameters:
thee Pointer to class AM
meth method choice (0=Forward Euler;1=Backward Euler;2=Trapezoidal Rule)
dt the time step
t0 the initial time
numstep number of the time steps
pfreq frequency of the printing contour
efreq frequency of energy printing
ekeytotal total number of printing energies
pdetype index for different types of PDEs:SIMP_TYPE/TDEP_TYPE/NLIN_TYPE
ltol error tolerance
lmax number of iterations to do (the maximum allowed)
vsock socket for writing a finite element mesh or mesh function

int AM_unRefine ( AM *  thee,
int  rkey,
int  pkey 
)

Un-refine the mesh.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
Success enumeration
Parameters:
thee Pointer to class AM
rkey Boolean sets the rkey type for un-refining the mesh.
pkey Boolean sets the pkey type to prolongate a vector

void AM_writeGEOM ( AM *  thee,
Vio *  sock,
int  defKey,
int  colKey,
int  chartKey,
double  gluVal,
int  fkey,
int  number,
char *  format 
)

Write out a mesh in some format.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
sock socket for reading the external mesh data (NULL otherwise)
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)
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
chartKey chartKey < 0 ==> draw all simplices chartKey >= 0 ==> draw only simplices with chart chartKey
gluVal gluVal == 1. ==> draw all simplices glued together 0. < gluVal < 1. ==> draw simplices with some separation
fkey fkey == 0 ==> draw simplices fkey == 1 ==> draw only simplex boundary faces fkey == 2 ==> draw only simplices with a boundary face
number the number of block work vector
format GV/MATH format

void AM_writeSOL ( AM *  thee,
Vio *  sock,
int  number,
char *  format 
)

Write out a solution in some format.

Author:
Michael Holst
Note:
Class AM: Non-inlineable methods (am.c)
Returns:
None
Parameters:
thee Pointer to class AM
sock socket for reading the external mesh data (NULL otherwise)
number the number of block work vector
format Pointer to GV/MATH format

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