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VECFEM3 Reference Manual: mesh
Type: format
NAME
mesh  data format of the VECFEM mesh
arrays
SYNOPSIS
 LIVEM, IVEM, LNEK, NEK, LRPARM, RPARM, LIPARM, IPARM,
LDNOD, DNOD, LRDPRM, RDPARM, LIDPRM, IDPARM, LNODN,
NODNUM, LNOD, NOD, LNOPRM, NOPARM,
 INTEGER
 LIVEM, LNEK, LRPARM, LIPARM, LDNOD, LRDPRM, LIDPRM, LNODN,
LNOPRM
 INTEGER
 IVEM(LIVEM), NEK(LNEK), IPARM(LIPARM), DNOD(LDNOD),
IDPARM(LIDPRM), NODNUM(LNODN)
 DOUBLE PRECISION
 RPARM(LRPARM), RDPARM(LRDPRM), NOD(LDNOD), NOPARM(LNOPRM)
PURPOSE
The mesh arrays describe the finite element mesh for the VECFEM tool. The arrays NEK, IPARM
and RPARM contain the information of the mesh topology,
the arrays DNOD, IDPARM and RDPARM
contain the information of the Dirichlet condition and NODNUM,
NOD and NOPARM contain the information of
the geometrical nodes of the FEM mesh. The array IVEM
contains the necessary information for the management of the mesh
arrays. It is also used to hand over special parameters to the
routines in the VECFEM library.
The mesh arrays have to be set by the user or to be read from
a data file by vemu02, idevem or patvem.
At the beginning the distribution of the data onto the processes
is arbitrary. The node id numbers refer to a numbering over all
processes. Before the calculation starts the mesh is prepared by
the subroutine vemdis. Especially the
id numbers of the geometrical nodes refer afterwards to a local
numbering on the process and the elements and Dirichlet
conditions are rearranged. In the description of the arguments,
values, which will be changed by the mesh preparation, are marked
by 'input/output' and unchanged values are marked by 'input'.
Values with marker 'global' have to be equal on all processes. 'Local'
values may vary on the processes.
The mesh arrays describe the geometry of the elements and so
the union of all elements describes the domain of the functional
equation. The needed information is called the 'geometrical mesh'.
On every element the method for the approximation of the solution
of the functional equation is defined by the information in the mesh
arrays, which are called 'proposal mesh'.
To introduce parameters into the definition of the functional
equations (e.g. material constants, temperature distributions)
the element oriented parameter sets IPARM and RPARM,
the Dirichlet condition oriented parameter sets IDPARM
and RDPARM and the geometrical node oriented parameter
set NOPARM should be used. The user can freely define
them. VECFEM ensures that the parameter
sets are always matched to resorting, renumbering and
distributions of the mesh arrays. See also userb,
userf, usrfu
and userl.
The linear forms used for the formulation of functional
equations are sums of integrals over the manifolds M(DIM),...,M(0),
where M(CLASS) is a manifold of dimension CLASS
for CLASS=0,...,DIM. The union of the
manifolds is covered by a set of points called the (global)
geometrical nodes. The array NOD specifies their
coordinates and NODNUM the corresponding id numbers.
The manifold M(CLASS) is covered by the elements of
dimension CLASS. GEOTYP global geometrical nodes
describe an element. The id numbers of these geometrical nodes
have to be specified in the array NEK. The succession
in which the geometrical nodes for an element have to be stored (called
the local (geometrical) node numbering) depends on the element
type and is described in the VECFEM
manual. The three parameters GEOTYP, FORM
and CLASS distinguish the different types of elements:
GEOTYP 
number of geometrical nodes 
FORM 
number of vertices of the element 
CLASS 
the dimension of the manifold the element
belongs to. 
The following table shows all geometrical element types of VECFEM and their parameters ('/' marks a
choice):
manifold 
element 
GEOTYP
for order 
FORM 
CLASS 


1 
2 
3 


point 
point 
1 
1 
1 
1 
0 
line 
line 
2 
3 
4 
2 
1 
area 
triangle 
3 
6 
9/10 
3 
2 

quadrilateral 
4 
8/9 
12/16 
4 
2 
body 
tetrahedron 
4 
10 
16 
4 
3 

prism 
6 
15 
24 
6 
3 

hexahedron 
8 
20 
32 
8 
3 
The element subdivision has to be selected such that for i=0,DIM
the restrictions of the elements used for the subdivision of a
manifold M(i) are also elements used for the subdivision of
manifolds M(j) of lower dimension 0<=j<i. Additionally you
have to consider that a node which is vertex/face node of any
element has also to be vertex/face node of every other element
containing this node. In general a mesh with elements of
different order is not possible.
For the definition of linear forms tangential spaces at the
manifolds can be used. In the case DIM=3, the first
tangential direction TAU(1) at a manifold M(2) points
from the first geometrical node of the element to the second one
and for quadrilateral/triangle elements the second tangential
direction TAU(2) points from the first geometrical
node of the element to the fourth/third one. In the case DIM=2,3,
the tangential direction TAU(1) at a manifold M(1)
points from the first geometrical node of the element to the
second one. If you use tangential directions in your linear forms
you have to take these conventions into consideration in the mesh
generation.
The proposal mesh defines the approximation of the NKvalued
solution of the functional equation. The union of the manifold M(DIM),...,M(0)
is covered by points called the global nodes. They are model only,
their coordinates do not have to be generated. In most cases
their coordinates are equal to the coordinates of the geometrical
nodes, but this is not necessary. On an element defined by the
geometrical mesh, the solution is interpolated by a polynomial
from its values at the global nodes in this element. The
interpolation polynomial is called 'proposal function'. The
global nodes, which are on the contact faces of the elements,
ensure that the approximation of the solution is continuous at
the contact faces. For every component the element needs the id
number of those NELTYP global nodes, which are used to
interpolate the solution component on this element. These id
numbers are also stored in the array NEK. The
succession in which the global nodes for an element have to be
stored (called the local node numbering) depends on the element
type and the type of the interpolation polynomial. It is
described in the VECFEM manual.
Currently VECFEM allows four
different types of polynomials on the elements characterised by
the value PRFLIB:
 Isoparametrical proposal functions (PRFLIB=0):
 On the element the global nodes are equal to the
geometrical nodes (NELTYP=GEOTYP).
The succession in the local numbering is the same. So the
geometry and the solution are represented in the same way,
which motivates the name 'isoparametrical'. It is the
usual selection of the proposal function. For a given
geometrical mesh the corresponding proposal mesh can be
generated by vemge2.
 Lagrangian proposal functions (PRFLIB=1):
 On every element the number of global nodes depends on
the order p>0 of the polynomial, which is used for the
interpolation of the solution. We recommend restricting p<6.
The following table gives the value of NELTYP
for prescribed order p:
elements 
NELTYP
for order p 
FORM 
CLASS 
point 
1 
1 
0 
line 
p+1 
2 
1 
triangle 
(p+1)(p+2)/2 
3 
2 
quadrilateral 
(p+1)² 
4 
2 
tetrahedron 
(p+1)(p+2)(p+3)/6 
4 
3 
prism 
(p+1)²(p+2)/2 
6 
3 
hexahedron 
(p+1)³ 
8 
3 
 The local numbering runs from the first geometrical node
in direction of the second global geometrical node, then
in direction of the third/fourth geometrical node for
triangle, tetrahedron and prism/ quadrilateral and
hexahedron elements and then in direction of the fourth/sixth/eighth
geometrical node for tetrahedron/ prism/ hexahedron
elements (more details in [THEOMAN])).
For a given geometrical mesh a suitable proposal mesh can
be generated by vemgen(later).
 Pieced isoparametrical proposal functions (PRFLIB=2):
 The locations of global nodes are selected like for PRFLIB=0,
but the proposal functions are piecewise polynomials with
reduced order int((p+1)/2) (e.g. order 1 > order 0,
order 2 > order 1 and order 3 > order 2) and a
subdivision into 2**CLASS subelements (more
details in [THEOMAN]).
The local numbering of the nodes is the same as for
isoparametrical proposal functions. For a given
geometrical mesh a suitable proposal mesh can be
generated by vemge2, if after
the vemge2 call PRFLIB=2
is set.
 Pieced Lagrangian proposal functions (PRFLIB=3):
 The locations of global nodes are selected like for PRFLIB=1,
but the proposal functions are piecewise polynomials with
reduced order int((p+1)/2) and a subdivision into 2**CLASS
subelements (more details in [THEOMAN]). The local
numbering of the nodes is the same as for Lagrangian
proposal functions. For a given geometrical mesh a
suitable proposal mesh can be generated by vemgen(later),
if after the vemgen(later) call PRFLIB=3 is
set.
VECFEM includes estimation for the error
of the solution approximation by a change of the proposal
function using the following table:
approximation 
error estimation 
note 
PRFLIB=0 
PRFLIB=2 
good performance but lower
estimation quality 
PRFLIB=1 
PRFLIB=3 
good performance but lower
estimation quality 
PRFLIB=2 
PRFLIB=0 
lower performance and good
estimation quality 
PRFLIB=3 
PRFLIB=1 
lower performance and good
estimation quality. 
The type of the proposal functions PRFLIB and the
order of the element NELTYP may be different for the
various components of the solution. Therefore NELTYP
and PRFLIB have NK components. This general
case is called a 'mixed finite element mesh' and is denoted by OWN=NK.
The global nodes are numbered over all components. Global nodes,
which have the same coordinates but are used for the
approximation of different components get different id numbers.
The number of unknowns is equal to the number of global nodes. In
many applications the same proposal functions are used for all
components. Then only the proposal mesh for the first component
has to be specified. This type of proposal mesh is called a 'componentbycomponent
numbering' and is denoted by OWN=1. It is useful for
periodical boundary conditions and high order approximations. The
number of unknowns is equal to the number of global nodes times
the number of components NK. If additionally the
global nodes are equal to the geometrical nodes, the proposal
mesh is called an 'isoparametrical mesh'. It is denoted by OWN=0.
In this case the geometrical mesh does not have to be specified.
Since it is easy to handle it is the usual mesh type. But you
have to keep in mind that there are some type of problems where
mixed meshes have to be used (e.g. NavierStokes equation).
The set of all elements, which are used to describe the domain
and to approximate the solution, is split into groups. In every
group all elements have the same (3+2*NK)tuple of
parameters (GEOTYP,FORM,CLASS,NELTYP,PRFLIB).
It is optimal to subdivide every manifold into elements of one
type. In many cases the use of more groups is unavoidable to
subdivide the body or to define material coefficients. VECFEM sets no limit to the number of
groups, but it should be kept as small as possible so that you
will get maximal efficiency.
ARGUMENTS
 LIVEM integer, scalar, input, local
 Length of the integer information vector, LIVEM>=
MESH+ DINFO* DINFO1.
 IVEM integer, array: IVEM(LIVEM),
input/output, local/global
 Integer information vector.
 (1)=MESH, input, local
 Start address of the mesh information in IVEM.
 (MESH), void, local
 Start of the mesh information.
 (MESH+1)=NDEG, input/output, local
 Number of geometrical nodes on the process.
 (MESH+2)=NK, input, global
 Number of the solution components.
 (MESH+3)=DIM, input, global
 Space dimension, DIM=1,2 or 3.
 (MESH+4)=NGROUP, input, global
 Number of element groups
 (MESH+5)=NN, input/output, local
 Leading dimension of the node array NOD, NN>=NDEG.
 (MESH+13)=NOP1, input/output, local
 Leading dimension of the node parameter array NOPARM,
NOP1>=NDEG.
 (MESH+14)=NOP, input, global
 Number of node parameters.
 (MESH+15)=OWN, input, global
 Mesh type.
0 
isoparametrical mesh. 
1 
the same approximation for all components,
componentbycomponent numbering of global nodes. 
NK 
individual approximation for the
components. 
 (MESH+18)=DIS, input/output, global
 Set DIS=0.
 (MESH+21)=GINFO, input, local
 Start address of group information in IVEM
relative to MESH, GINFO>=30.
 (MESH+22)=GINFO1, input, local
 Number of information per group, GINFO1>=23+2*NK.
 (MESH+23)=DINFO, input, local
 Start address of information for Dirichlet conditions in IVEM
relative to MESH, DINFO>=GINFO+
GINFO1*NGROUP.
 (MESH+24)=DINFO1, input, local
 Number of information per component, DINFO1>=14.
Now the information for group g follow, g=1,NGROUP,
ng= MESH+GINFO+ GINFO1*
(g1):
 (ng)=NE, input/output, local
 Number of elements in group g on the process.
 (ng+1)=GEOTYP, input, global
 Number of geometrical nodes in the elements. In the case
of an isoparametrical mesh it does not have to be
specified.
 (ng+2)=FORM, input, global
 Number of vertices of the elements.
 (ng+3)=CLASS, input, global
 Dimension of the elements.
 (ng+4)=ADDGEO, input/output, local
 Start address of the geometrical node numbers describing
the elements in NEK. In the case of an
isoparametrical mesh it does not have to be specified.
 (ng+5)=GEO1, input/output, local
 Leading dimension of geometrical node numbers describing
the elements, normally GEO=NE. In
the case of an isoparametrical mesh it does not have to
be specified.
 (ng+7)=ADRSP, input/output, local
 Start address of the real scalar parameters in RPARM.
 (ng+8)=NRSP, input, global
 Number of the real scalar parameters.
 (ng+9)=ADRVP, input/output, local
 Start address of the real vector parameters in RPARM.
 (ng+10)=RVP1, input/output, local
 Leading dimension of the real vector parameters, normally
RVP1=NE.
 (ng+11)=NRVP, input, global
 Number of the real vector parameters per element.
 (ng+12)=ADISP, input/output, local
 Start address of the integer scalar parameters in IPARM.
 (ng+13)=NISP, input, global
 Number of the integer scalar parameters.
 (ng+14)=ADIVP, input/output, local
 Start address of the integer vector parameters in IPARM.
 (ng+15)=IVP1, input/output, local
 Leading dimension of the integer vector parameters,
normally IVP1=NE.
 (ng+16)=NIVP, input, global
 Number of the integer vector parameters per element.
 (ng+20)=ADDNEK, input/output, local
 Start address of the global node numbers describing the
elements in NEK.
 (ng+21)=NEK1, input/output, local
 Leading dimension of the global node numbers describing
the nodes.
For d=1,max(OWN,1) the approximation
polynomials for the solution have to be defined for group
g:
 (ng+22+d)=NELTYP, input, global
 Number of local nodes in the elements for component d.
 (ng+22+NK+d)=PRFLIB, input, global
 Selection of the element library.
0 
isoparametrical elements. 
1 
Lagrangian proposal functions. 
2 
pieced isoparametrical elements with half
the element size and half the order. 
4 
pieced Lagrangian proposal functions with
half the element size and half the order. 
 Now the information for the Dirichlet conditions of
component d follow, d=1,NK, nd= MESH+DINFO+
DINFO1* (d1):
 (nd)=NDC, input/output, local
 Number of Dirichlet conditions for component d on the
process.
 (nd+1)=ADDCG, input/output, local
 Start address of the geometrical node numbers of the
Dirichlet conditions in DNOD.
 (nd+2)=ADDC, input/output, local
 Start address of the global node numbers of the Dirichlet
conditions in DNOD.
 (nd+3)=ADRSP, input/output, local
 Start address of the real scalar parameters for the
Dirichlet conditions in RDPARM.
 (nd+4)=NRSDP, input, global
 Number of the real scalar parameters for the Dirichlet
conditions.
 (nd+5)=ADRVDP, input/output, local
 Start address of the real vector parameters for the
Dirichlet conditions in RDPARM.
 (nd+6)=RVDP1, input/output, local
 Leading dimension of the real vector parameters for the
Dirichlet conditions, normally RVDP1=NDC.
 (nd+7)=NRVDP, input, global
 Number of the real vector parameters for the Dirichlet
conditions.
 (nd+8)=ADISDP, input/output, local
 Start address of the integer scalar parameters for the
Dirichlet conditions in IDPARM.
 (nd+9)=NISDP, input, global
 Number of the integer scalar parameters for the Dirichlet
conditions.
 (nd+10)=ADIVDP, input/output, local
 Start address of the integer vector parameters for the
Dirichlet conditions in IDPARM.
 (nd+11)=IVDP1, input/output, local
 Leading dimension of the integer vector parameters for
the Dirichlet conditions, normally IVDP1=NDC.
 (nd+12)=NIVDP, input, global
 Number of the integer vector parameters for the Dirichlet
conditions.
 LNEK integer, scalar, input, local
 Length of the element array.
 NEK integer, array: NEK(LNEK),
input/output, local
 Array of the elements on the process. NEK
contains the key list to define the geometrical mesh and
the proposal mesh. For the elements in group g the id
numbers of the geometrical nodes describing the elements
start at position ADDGEO:
NEK(ADDGEO1+GEO1*(i1)+z)
= 
id number of the ith geometrical node
for the zth element in group g, 
 where i=1,...,GEOTYP and z=1,...NE.
GEO1 is greater or equal NE and
should be odd. In the case of an isoparametrical mesh the
geometrical mesh does not have to be specified. For the
elements in group g the id numbers of the global nodes
which are used for the approximation of the component d
start at position ADDNEK+NEK1*S,
where S is the sum of all NELTYP for the
components 0<c<d. NEK1 is greater or
equal NE and should be odd.
NEK(ADDNEK1+NEK1*(i1+S)+z)= 
id number of the ith global node for the
zth element and component d in group g, 
 where i=1,...,NELTYP and z=1,...NE.
In the case of a componentbycomponent numbering and an
isoparametrical mesh, only the global nodes for the first
component have to specified (S=0!).
 LRPARM integer, scalar, input, local
 Length of the real parameter array.
 RPARM double precision, array: RPARM(LRPARM),
input/output, local
 Real parameter array. To every group g the user can
assign a set of NRSP real values called 'real
scalar parameters', and to every element in group g the
user can assign a set of NRVP real values
called 'real vector parameters'. Using these parameter
sets, values (e.g. material properties, nodal forces) are
handed over to the user routines. The real scalar
parameters define a homogeneous and the real vector
parameters specify a nonhomogeneous value distribution.
The real scalar parameters are stored in RPARM
starting at ADRSP:
RPARM(ADRSP1+i)= 
the ith real scalar parameter for group
g, 
 where i=1,...,NRSP. The real vector parameters
are stored in RPARM starting at ADRVP:
RPARM(ADRVP1+RVP1*(i1)+z)= 
the ith real vector parameter for the zth
element for group g, 
 where i=1,...,NRVP and z=1,...NE
and RVP1 is greater or equal NE.
The real scalar parameters have to be equal on all
processes.
 LIPARM integer, scalar, input, local
 Length of the integer parameter array.
 IPARM integer, array: IPARM(LIPARM),
input/output, local
 Integer parameter array. To every group g the user can
assign a set of NISP integer values called 'integer
scalar parameters', and to every element in group g the
user can assign a set of NIVP integer values
called 'integer vector parameters'. The vector integer
parameters should be used to assign a unique number over
all processes to every element. This element number is
necessary if you hand over the FEM mesh to a
postprocessor, see vemide, vempat. Additional integer vector
parameters can be used to distinguish different material
properties in a group, e.g. the value 1 for the second
integer vector parameters marks steel, the value 2 marks
iron, and so on. The integer scalar parameters are stored
in IPARM starting at ADISP:
IPARM(ADISP1+i)= 
the ith integer scalar parameter for
group g, 
 where i=1,...,NISP. The integer vector
parameters are stored in IPARM starting at ADIVP:
IPARM(ADIVP1+IVP1*(i1)+z)= 
the ith integer vector parameter for the
zth element for group g, 
 where i=1,...,NIVP and z=1,...NE
and IVP1 is greater or equal NE.
The integer scalar parameters have to be equal on all
processes.
 LDNOD integer, scalar, input, local
 Length of the array of the Dirichlet nodes.
 DNOD integer, array: DNOD(LDNOD),
input/output, local
 Array of the Dirichlet nodes on the process. For every
component d the id numbers of the global nodes where
Dirichlet conditions are prescribed have to be specified.
They represent the support D(d) of the Dirichlet
condition in the definition of the functional equations,
see veme00, veme02 and vemp02.
Starting at ADDC the id numbers of the NDC
global nodes are stored. The id numbers of the
corresponding geometrical nodes start at ADDCG:
DNOD(ADDCG1+z)= 
number of the geometrical node of the zth
Dirichlet condition for component d 
DNOD(ADDC1+z)= 
number of the global node of the zth
Dirichlet condition for component d 
 where z=1,...NDC. In the case of an
isoparametrical mesh the global node numbers do not have
to be specified. If you use a mesh of order one to
describe the geometrical structures but a order two
approximation of the solution it will be necessary to
introduce geometrical nodes which are not referred to by
the geometrical representation of the elements. If you do
not use the location of the Dirichlet conditions (e.g. if
it is constant zero) it is not necessary to introduce new
geometrical nodes. Set the id number of the geometrical
node to 1.
 LRDPRM integer, scalar, input, local
 Length of the real Dirichlet parameter array.
 RDPARM double precision, array: RDPARM(LRDPRM),
input/output, local
 Array of the real Dirichlet parameters. To every
component d the user can assign a set of NRSDP
real values called 'real scalar Dirichlet parameters',
and to every Dirichlet condition for component d the user
can assign a set of NRVDP real values called 'real
vector Dirichlet parameters'. Using these Dirichlet
parameter sets, values (e.g. the values of the prescribed
function, defined by userb) are
handed over to the user routines. The real scalar
Dirichlet parameters are stored in RDPARM
starting at ADRSDP:
RDPARM(ADRSDP1+i)= 
the ith real scalar Dirichlet parameter
for component d, 
 where i=1,...,NRSDP. The real vector Dirichlet
parameters are stored in RDPARM starting at ADRVDP:
RDPARM(ADRVDP1+RVP1*(i1)+z)= 
the ith real vector Dirichlet parameter
for the zth Dirichlet condition for component d, 
 where i=1,...,NRVDP and z=1,...NDC
and RVP1 is greater or equal NDC.
The real scalar Dirichlet parameters have to be equal on
all processes.
 LIDPRM integer, scalar, input, local
 Length of the integer Dirichlet parameter array.
 IDPARM integer, array: IDPARM(LIDPRM),
input/output, local
 Array of the integer Dirichlet parameters. To every
component d the user can assign a set of NISDP
integer values called 'integer scalar Dirichlet
parameters', and to every Dirichlet condition in
component d the user can assign a set of NIVDP
integer values called 'integer vector Dirichlet
parameters'. The integer vector Dirichlet parameters can
be used to distinguish different types of Dirichlet
conditions for one component. E.g. in a rectangle domain
with Dirichlet conditions on its border, the value 1 for
the first integer vector Dirichlet parameter marks
Dirichlet conditions at the top boundary, the value 2
marks the right boundary and so on. The integer scalar
Dirichlet parameters are stored in IDPARM
starting at ADISDP:
IDPARM(ADISDP1+i)= 
the ith integer scalar Dirichlet
parameter for component d, 
 where i=1,...,NISDP. The integer vector
Dirichlet parameters are stored in IDPARM
starting at ADIVDP:
IDPARM(ADIVDP1+IVP1*(i1)+z)= 
the ith integer vector Dirichlet
parameter for the zth Dirichlet condition for component
d, 
 where i=1,...,NIVDP and z=1,...NDC
and IVP1 is greater or equal NDC.
The integer scalar Dirichlet parameters have to be equal
on all processes.
 LNODN integer, scalar, input, local
 Length of the array of the id numbers of the geometrical
nodes, LNODN>=NDEG.
 NODNUM integer, array: NODNUM(LNODN),
input/output, local
 Array of the id numbers of the geometrical nodes on the
process. The geometrical nodes used on the process are
continuously numbered from 1 to NDEG.
Additionally there is a numbering of the geometrical
nodes over all processes (it need not be continuous). NODNUM(i)
is the global geometrical node id number over all
processes of the geometrical node with local node id i on
the process. Normally a global geometrical node id is
referred to by more than one process.
 LNOD integer, scalar, input, local
 Length of the array of the coordinates of the geometrical
nodes on the process, LNOD>=DIM*NN.
 NOD double precision, array: NOD(LNOD),
input/output, local
 Array of the coordinates of the geometrical nodes. For
the geometrical node with id i on the process we have
NOD(i )= 
x1coordinate, 
NOD(i+ NN)= 
x2coordinate, 
NOD(i+2*NN)= 
x3coordinate, 
 where i=1,...,NDEG. If two processes refer to
the same global geometrical node via the NODNUM
vector (this is a normal situation), any of the both
specified node coordinates on the processes is selected
during the element distribution.
 LNOPRM integer, scalar, input, local
 Length of the array of the node parameters, LNOPRM>=
NOP1* NOP.
 NOPARM double precision, array: NOPARM(LNOPRM),
input/output, local
 Array of the node parameters for the geometrical nodes on
the process. In many cases the linear forms depend on a NOPvalued
function (e.g. a temperature distribution). It is given
at the geometrical nodes. So NOP real values
are allocated to every geometrical node. They are called
the (real) node parameters. We have
NOPARM(NOP1*(j1)+i)= 
the jth parameter at the ith node on
the process, 
 where i=1,NDEG and j=1,NOP1. The
node parameters are interpolated at the elements by
polynomials. The evaluations of this polynomial and its
derivatives is handed over to the user routines, see userf, userl
usrfu and userb.
If two processes refer to the same global geometrical
node via the NODNUM vector (this is a normal
situation), one of the two specified node parameter sets
on the processes is arbitrarily selected during the
element distribution.
EXAMPLE
See vemexamples.
REMARKS
 The elements are distributed to the processes to get good
load balancing, and on every process the elements are
resorted to get good vectorization (blocking). The
efficiency is maximal if you avoid containing the same
geometrical and global nodes in a large number of
elements.
 The set of the distances of the global node numbers in
all elements is called the diagonals of the mesh. To get
optimal efficiency in lsolpp
the cardinality of the diagonals should be as small as
possible. This is called a diagonal optimal numbering of
the global nodes (a bandwidth optimal numbering has a
minimal bound for the diagonal numbers). If you expect a
large number of diagonals you should use the bandwidth
optimizer vemopt(later) to reduced the number of
diagonals.
 The parameter sets NOPARM, RPARM, IPARM,
RDPARM and IDPARM are insignificant
for VECFEM. vemdis resorts them in the element
distribution and block procedure and hands them over to
the user routines, see userb userb, userf,
usrfu and userl.
They get their significance by the statements in your
routines, which define the linear forms and the Dirichlet
conditions.
INTERNAL
The following entries in the IVEM are set by vemdis.
 (19)=XVEM, input, global
 If XVEM=30841, the error messages are printed
with respect of vembuild and xvem.
 (MESH+6)=NNEK, output, local
 Used storage in the element array NEK.
 (MESH+7)=NRPARM, output, local
 Used storage in the real element parameter array RPARM.
 (MESH+8)=NIPARM, output, local
 Used storage in the integer element parameter array IPARM.
 (MESH+9)=NDNOD, output, local
 Used storage in the Dirichlet condition array DNOD.
 (MESH+10)=NRDPRM, output, local
 Used storage in the real Dirichlet parameter array RDPARM.
 (MESH+11)=NIDPRM, output, local
 Used storage in the integer Dirichlet parameter array DPARM.
 (MESH+12)=NINFO, output, local
 Used storage in IVEM for the mesh information,
NINFO= DINFO+ NK* DINFO1+
2+3*NPROC+ NGROUP+ NBLK.
 (MESH+16)=LM, output, global
 Maximal number of global nodes on a process.
 (MESH+18)=DIS, output, global
 DIS=220964 indicates a distributed mesh. If DIS<>220964,
the numbering of the geometrical nodes refers to
numbering over all processes.
 (MESH+19)=SORTI, output, local
 Start address of resort information in IVEM
relative to MESH, SORTI=DINFO+DINFO1*NK.
Now the information for group g follow, g=1,NGROUP,
ng= MESH+GINFO+ GINFO1*
(g1):
 (ng+22)=TOTNT, output, global
 Total number of global nodes for the element in group g.
 (MESH+SORTI)=NJUMP,
output, global
 Number of communication cycles to consider all mesh
couplings.
 (MESH+SORTI+1)=NBLK,
output, local
 Number of element blocks on the process.
 (MESH+SORTI+1+p)=JUMP,
output, global
 MYPROC+JUMP(p) is target of the pth
communication cycle, p=1,NJUMP.
 (MESH+SORTI+NPROC+1+p)=LMATBK,
output, global
 LMATBK(p) is the number of global nodes on
process p, p=1,NPROC.
 (MESH+SORTI+2*NPROC+1+p)=PTRMBK,
output, global
 PTRMBK(p)+1 is the first global node on
process p, p=1,NPROC.
 (MESH+SORTI+3*NPROC+1+g)=BLKLST,
local, global
 Number of element blocks in group g, g=1,NGROUP.
 (MESH+SORTI+3*NPROC+1+NGROUP+i)=BLK,
output, local
 Length of element block i, i=1,NBLK.
 (MESH+SORTI+3*NPROC+1+NGROUP+NBLK),
output, local
 End of mesh information.
REFERENCES
[FAQ], [THEOMAN], [DATAMAN], [DATAMAN2], [P_MPI].
ALSO SEE
VECFEM, vemexamples.
COPYRIGHTS
Program by L. Grosz, C. Roll, P. Sternecker, 19891996. Copyrights by
Universitaet Karlsruhe 19891996. Copyrights by Lutz Grosz 1996.
All rights reserved. More details see VECFEM.
By L. Grosz, Auckland, 31 May, 2000.
