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PROGRAM:

NAME

bamg - bidimensional anisotropic mesh generator

SYNOPSIS

bamg options -g input[.bamgcad] -o ouput[.bamg]

EXAMPLE

Generate the mesh of a square ]1,1[^2 with a mesh size h=0.666 at all vertices. Enter the
unix command:

bamg -g toto.bamgcad -o toto.bamg

The geometry in defined in the square.bamgcad file:

MeshVersionFormatted 0
Dimension 2
Vertices 4
-1 -1 1
1 -1 2
1 1 3
-1 1 4
Edges 4
1 2 1
2 3 2
3 4 3
4 1 4
hVertices
0.666 0.666 0.666 0.666

The file starts with vertices, coordinates and identifier. Then come the boundary edges,
using vertices identifiers and defining a boundary edge identifier.

OUTLINE

This software can

1) create
a mesh from a geometry

2) adapt
a mesh from an existing background mesh using a metric or a solution file.

3) metric build
just build a metric file, e.g. if you have an other mesher .

3) quality improve
of an existing mesh, by generating a new mesh.

5) interpolate
a field from one mesh to another.

1) CREATE

Create a mesh from a geometry. Example:

bamg -g toto.bamgcad -o toto.bamg

-g filename
the input file, specifying tghe geometry boundaries of the domain to mesh (bamg
file format DB mesh).

-o filename
the output mesh file (bamg file format DB mesh). Some alternatives output file
formats are supported with some -oXY options where XY is one of the supported
output file formats (see below). In addition, optional parameter can be added to
specify a metric or the quality improvement. All the options are described below.

2) ADAPT

Adapt a mesh from a background mesh using a metric or solution file. Example:

bamg -b toto_bgd.bamg -Mbb toto_bgd_sol.bb -o toto_new.bamg

-b filename
the input background mesh, where the file suffixe defines the format of the file:
.amdba, .am_fmt, .am, .ftq, .nopo. Otherwise the file is the bamg default BD mesh
file format.

-Mbb filename

-MBB filename

-M filename
The input metric file. The -Mbb or -MBB specifies the solution file from which the
metric is automatically computed, where the file is of type bb or BB (see file
format below). An alternative is to specify directly the metric with the -M option
(file format Metric).

-o filename
the output mesh file (bamg file format DB mesh). Some alternatives output file
formats are supported with some -oXY options where XY is one of the supported
output file formats (see below). In addition, optional parameter can be added to
control the metric generation and the quality improvement. All the options are
described below.

3) METRIC BUILD

Construct a metric file for an existing mesh and with a provided solution. This option can
be used without generating a new mesh, e.g. if you have an other mesher.

bamg -r toto_bgd.bamg -Mbb toto_bgd_sol.bb -oM toto_bgd.metric

-r filename
The input mesh file (bamg format DB mesh).

--Mbb filename

--MBB filename
The input provided solution, where the file is of type bb or BB (see file format
below).

-oM filename
The output metric file, in file format Metric (see file format below). In
addition, optional parameter can be added to control the metric generation. All
the options are described below.

4) QUALITY IMPROVE

Improve quality for an existing mesh and generate a new mesh.

bamg -r toto_bgd.bamg -M toto_bgd.metric -o toto_new.bamg

-r filename
The input mesh file (bamg format DB mesh).

-M filename
The input metric file, in file format Metric (see file format below).

-o filename
the output mesh file (bamg file format DB mesh). Some alternatives output file
formats are supported with some -oXY options where XY is one of the supported
output file formats (see below). In addition, optional parameter can be added to
control the quality improvement. All the options are described below.

5) INTERPOLATE

In the adaption process, a solution has been computed with the background mesh. In order
to transfer the solution of the problem under consideration on the new generated mesh, an
interpolation of old solution is necessary. This tranferred solution may be a good initial
guess for the solution on the new mesh. This interpolation is carried out in a P1 Lagrange
context.

bamg -b toto_old.bamg -rbb toto_old.bb -r toto_new.bamg -obb toto_new.bb

-b filename
The destination input mesh file (bamg format DB mesh).

-rbb filename

-rBB filename
The origin input solution, where the file is of type bb or BB (see file format
below).

-r filename
The origin input mesh file (bamg format DB mesh).

-wbb filename

-wBB filename
The output solution,as reinterpolated on the destination mesh.

CREATION OPTIONS

-hmax float
Set the value of the maximal edge size. Default value is the diameter of the
domain to be meshed.

-hmin float
Set the value of the minimal edge size. Default value is related to the size of
the domain to be meshed and the grid resolution used by the mesh generator (machine
dependent).

-errg float
Set the value of the relative error on geometry of the boundary. Default value is
0.1. In any case this value is geater than 1/sqrt(2). Remark that mesh size
created by this option can be smaller than the hmin argument due to geometrical
constraint.

-nbv int
Set the maximal number of vertices of the generated mesh. Default value is 50000.

ADAPTATION OPTIONS

These options are relevant when computing a metric from a scalar field provided in a .bb
file. Notice that, when providing a tensor metric in the .bb file, the metric computation
is not performed and these options are not relevent.

-RelError
compute the metric with a relative error. This is the default. In this case, the
metric field is defined by

1 |H(x)|
M(x) = ---------- --------------------
err*coef^2 max(CutOff,|eta(x)|)

where err, coef, CutOff are adjustable parameters defined below, eta is the
solution field read in the input file and H is its Hessian. Here |eta| denotes the
absolute value of the field eta and |H| is the tensor field composed of the
absolute values of the Hessian eigenvalues and with the same eigenbasis as H.

-AbsError
compute the metric with an absolute error. In this case, the metric is defined by

1 |H(x)|
M(x) = ---------- ---------------------
err*coef^2 (sup(eta) - inf(eta))

where sup(eta) and inf(eta) denotes the two extremal values of the input solution
field eta.

-coef float
the multiplicative coefficient on the mesh size. Default value is 1.0.

-err float
the level of the P1 interpolation error. Default value is 0.01. Recall that this
error behaves as O(h^2) locally, where h is the local mesh size. Remark on the two
previous formulae that a change by a factor 1/4 is equivalent to a change by a
factor 1/2 on the mesh size. So, either coef or err are specified in order to
generate a convergent mesh family.

-CutOff float
the cut-off value used for the relative error criteria. Default value is 1e-5.

-power float
Set the power parameter of hessien to construct the metric. Default value is 1.

-NbJacobi int
Set the number of iterations in a smoothing procedure during the metric
construction. The 0 value implies no smoothing. Default value is 1.

-ratio float
Set the ratio for a prescribed smoothing on the metric. If ratio is 0 (default
value) or less than 1.1, no smoothing on the metric is done. If ratio > 1.1 the
speed of mesh size variation is bounded by log(ratio). Remark tht, as val is
closer to 1, the number of vertices generated increases. This may be useful to
control the thickness of refined regions near shocks or boundary layers.

-aniso

-iso The -anio enforces the metric to be anisotropic. This is the default. Conversely,
the metric may be of isotropic type with the -iso flag.

-anisomax float
Set the bound of mesh anisotropy with respect to minimal mesh size in all direction
so the maximal mesh size in all direction is bounded by the ratio anisomax. The
default value is 1e6. Remark that when anisomax=1, the generated mesh is
isotropic.

-hminaniso float
Set the value of hmin the minimal edge size and set the aniso mode.

-maxsubdiv float
Change the metric such that the maximal subdivision of a background's edge is bound
by the maxsubdiv number. The maxsubdiv number is alway limited by 10 and this is
the default value.

-KeepBackVertices

-noKeepBackVertices
Try to Keep old vertices (default). Otherwise, all vertices are created from
scratch.

-NoRescaling

-Rescaling
Don't rescale the solution between [0,1] before metric computation Default is to
rescale.

QUALITY IMPROVEMENT OPTIONS

-NbSmooth int
Set the number of iterations of the mesh smoothing procedure. Default value is 3.

-omega float
Set the relaxation parameter of the smoothing procedure, Default value is 1.8.

-splitpbedge

-nosplitpbedge
Sometimes, an internal edge can have its two vertices on the boundary. This causes
a triangle to have all its vertices on the boundary. With the -splitpbedge option,
this edge is splited in two, and this situation is avoided. By default, don't
split.

-thetaquad float
to create quad with 2 triangles Merge two triangles into a quadrilateral when the
four angles of the quadrilateral are in the range [thetaquad, 180-thetaquad].

-2 to create the mesh with a mesh size divided by two.

-2q to split all triangles in three quadrilaterls, and to split all quadrilaterals in
four.

OUTPUT MESH FORMAT OPTIONS

-o filename
bamg DB mesh file format (default).

-oamdba filename
amdba format.

-oftq filename
ftq format.

-omsh filename
msh format (freefem3 format).

-oam_fmt filename
am_fmt format.

-oam filename
am format.

-onopo filename
nopo format.

OTHERS OPTIONS

-thetamax float
Set the angular limit for a corner in degre to be curved. The angle is defined
from two normals of two concecutives edges. The default is 180 degree, i.e. no
corners are curved. This option is usefull when no geomtry are provided, e.g.
remeshing from an other mesh file format (am_fmt, amdba, nopo, etc). This
parameter is normaly specified in the geometry boundaries file (in BD file format)
by the AngleOfCornerBound optional section: when this file format is used, this
option has no effet.

-v int Set the level of printing (verbosity), which can be chosen between 0 and 10.
Default value is 1.

GEOMETRY FILE FORMAT (BAMGCAD)

The general structure allows to specify a mesh describing the geometry of the given
domain. The identification of the boundaries are used to define boundary conditions for a
partial derivative equation problem. In this case, some of the above sections are not
relevant. First the required sections are:

MeshVersionFormatted 0
Dimension 2
Vertices nv
{x_k y_k i_k} k=1:nv
Edges ne
{i_l j_l k_l} l=1:ne

Next, the optional sections:

SubDomain nd
{2 ie_k orient_k id_k} k=1:nd

A sub-domain, i.e. a bounded connex components of the plan is defined using one edge
identifier ie along with an orientation information orient, indicating on which side of
this entity the sub-domain lies. This feature is usefull, e.g. when dealing with a domain
with holes. The sub-domain number is id. If no sub-domain are defined, then we suppose
to mesh all the bounded connex component of the plan. Remark: SubDomainFromGeom is
equivalent to SubDomain.

AngleOfCornerBound angle

The AngleOfCornerBound specifies the angular limit for a corner in degre to be curved.
The angle is defined from two normals of two concecutives edges. The default is 180
degree, i.e. no corners are curved. When this angle is defined, some corners could be
specified not to be curved by

Corners nc
{i_k} k=1:nc

The curved geometric representation of a boundary in two dimensions uses the edges
provided in the data structure so as to define some curves of order three in the following
way:

* an edge whose endpoints are corners and if no additional information are provided
will be represented by a straight segment,

* an edge whose endpoints are corners but whose tangent is provided at one endpoint
will be represented by a curve of degree two,

* an edge whose endpoints are corners but whose tangents are provided at these
corners will be represented by a curve of degree three,

* an edge whose endpoints are not corners and with no additional information will be
represented by a curve of degree three. Indeed, we use in this case the adjacent
edges so as to evaluate the tangents at the edge endpoints.

In short, an edge defined by two informations will be approached by a straight line, three
information allow to obtain a curve of degree two and four data allow for a approximation
of degree three. The tangents are optionally specified by:

TangentAtEdges nt
{ie_k ive_k xt yt} k=1:nt

For the edge identifier ie, the tangent at its ive vertex (ive takes value 1 or 2) is
specified by its components xt and yt. Giving the tangent vector of an edge by means of
the tangent vector at a point enables us to deal with the case where several edges
(boundary lines) are emanating from a point.

The required vertices, are the vertices of the support that must be present in the mesh as
element vertices. Similarly, some edges can be required:

RequiredVertices nrv
{iv_k} k=1:nrv
RequiredEdges (nre
{ie_k} k=1:nre

The following features are planed for future work. For periodic boundary conditions, the
section EquivalencedEdges indicates that two edges must be meshed the same way:

EquivalencedEdges nee
{ie1_k ie2_k} k=1:nee

Crack definition is the purpose of the CrackedEdges section. We specify then that an edge
is identical in terms of geometry to another edge:

CrackedEdges nce
{ie1_k ie2_k} k=1:nce

CREDITS

Frederic Hecht <[email protected]> is the author of bamg. Pierre Saramito
<[email protected]> writes this unix man page.

MORE READING

The original site of the bamg mesh generator is http://www.ann.jussieu.fr/hecht/ftp/bamg.
Please read http://www.ann.jussieu.fr/hecht/ftp/bamg/bamg.pdf for the detailled file
formats and more advanced examples, e.g. a mesh adaptation loop to minimize the P1
Lagrange interpolation error.

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