Provided by: rheolef_6.7-6_amd64

**NAME**

bamg- bidimensional anisotropic mesh generator

**SYNOPSIS**

bamgoptions-ginput[.bamgcad] -oouput[.bamg]

**EXAMPLE**

Generate the mesh of a square]1,1[^2with a mesh sizeh=0.666at all vertices. Enter the unix command: bamg -g toto.bamgcad -o toto.bamg The geometry in defined in thesquare.bamgcadfile: 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 can1)createa mesh from a geometry2)adapta mesh from an existing background mesh using a metric or a solution file.3)metricbuildjust build a metric file, e.g. if you have an other mesher .3)qualityimproveof an existing mesh, by generating a new mesh.5)interpolatea field from one mesh to another.

**1)** **CREATE**

Create a mesh from a geometry. Example: bamg -g toto.bamgcad -o toto.bamg-gfilenamethe input file, specifying tghe geometry boundaries of the domain to mesh (bamg file formatDBmesh).-ofilenamethe output mesh file (bamg file formatDBmesh). Some alternatives output file formats are supported with some-oXYoptions whereXYis 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-bfilenamethe 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 defaultBDmeshfile format.-Mbbfilename-MBBfilename-MfilenameThe input metric file. The-Mbbor-MBBspecifies the solution file from which the metric is automatically computed, where the file is of typebborBB(see file format below). An alternative is to specify directly the metric with the-Moption (file formatMetric).-ofilenamethe output mesh file (bamg file formatDBmesh). Some alternatives output file formats are supported with some-oXYoptions whereXYis 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-rfilenameThe input mesh file (bamg formatDBmesh).--Mbbfilename--MBBfilenameThe input provided solution, where the file is of typebborBB(see file format below).-oMfilenameThe output metric file, in file formatMetric(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-rfilenameThe input mesh file (bamg formatDBmesh).-MfilenameThe input metric file, in file formatMetric(see file format below).-ofilenamethe output mesh file (bamg file formatDBmesh). Some alternatives output file formats are supported with some-oXYoptions whereXYis 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-bfilenameThe destination input mesh file (bamg formatDBmesh).-rbbfilename-rBBfilenameThe origin input solution, where the file is of typebborBB(see file format below).-rfilenameThe origin input mesh file (bamg formatDBmesh).-wbbfilename-wBBfilenameThe output solution,as reinterpolated on the destination mesh.

**CREATION** **OPTIONS**

-hmaxfloatSet the value of the maximal edge size. Default value is the diameter of the domain to be meshed.-hminfloatSet 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).-errgfloatSet 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 thehminargument due to geometrical constraint.-nbvintSet 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.-RelErrorcompute 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)|) whereerr,coef,CutOffare adjustable parameters defined below,etais the solution field read in the input file andHis its Hessian. Here|eta|denotes the absolute value of the fieldetaand|H|is the tensor field composed of the absolute values of the Hessian eigenvalues and with the same eigenbasis asH.-AbsErrorcompute 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)) wheresup(eta)andinf(eta)denotes the two extremal values of the input solution fieldeta.-coeffloatthe multiplicative coefficient on the mesh size. Default value is 1.0.-errfloatthe level of theP1interpolation error. Default value is 0.01. Recall that this error behaves asO(h^2)locally, wherehis 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, eithercoeforerrare specified in order to generate a convergent mesh family.-CutOfffloatthe cut-off value used for the relative error criteria. Default value is 1e-5.-powerfloatSet the power parameter of hessien to construct the metric. Default value is 1.-NbJacobiintSet the number of iterations in a smoothing procedure during the metric construction. The 0 value implies no smoothing. Default value is 1.-ratiofloatSet 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-isoThe-anioenforces the metric to be anisotropic. This is the default. Conversely, the metric may be of isotropic type with the-isoflag.-anisomaxfloatSet 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 ratioanisomax. The default value is 1e6. Remark that whenanisomax=1, the generated mesh is isotropic.-hminanisofloatSet the value ofhminthe minimal edge size and set the aniso mode.-maxsubdivfloatChange the metric such that the maximal subdivision of a background's edge is bound by themaxsubdivnumber. Themaxsubdivnumber is alway limited by 10 and this is the default value.-KeepBackVertices-noKeepBackVerticesTry to Keep old vertices (default). Otherwise, all vertices are created from scratch.-NoRescaling-RescalingDon't rescale the solution between[0,1]before metric computation Default is to rescale.

**QUALITY** **IMPROVEMENT** **OPTIONS**

-NbSmoothintSet the number of iterations of the mesh smoothing procedure. Default value is 3.-omegafloatSet the relaxation parameter of the smoothing procedure, Default value is 1.8.-splitpbedge-nosplitpbedgeSometimes, 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-splitpbedgeoption, this edge is splited in two, and this situation is avoided. By default, don't split.-thetaquadfloatto 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].-2to create the mesh with a mesh size divided by two.-2qto split all triangles in three quadrilaterls, and to split all quadrilaterals in four.

**OUTPUT** **MESH** **FORMAT** **OPTIONS**

-ofilenamebamg DB mesh file format (default).-oamdbafilenameamdba format.-oftqfilenameftq format.-omshfilenamemsh format (freefem3 format).-oam_fmtfilenameam_fmt format.-oamfilenameam format.-onopofilenamenopo format.

**OTHERS** **OPTIONS**

-thetamaxfloatSet 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 theAngleOfCornerBoundoptional section: when this file format is used, this option has no effet.-vintSet 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 Verticesnv{x_ky_ki_k}k=1:nvEdgesne{i_lj_lk_l}l=1:neNext, the optional sections: SubDomainnd{2ie_korient_kid_k}k=1:ndA sub-domain, i.e. a bounded connex components of the plan is defined using one edge identifieriealong with an orientation informationorient, 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 isid. If no sub-domain are defined, then we suppose to mesh all the bounded connex component of the plan. Remark:SubDomainFromGeomis equivalent toSubDomain. AngleOfCornerBoundangleTheAngleOfCornerBoundspecifies 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 Cornersnc{i_k}k=1:ncThe 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: TangentAtEdgesnt{ie_kive_kxtyt}k=1:ntFor the edge identifierie, the tangent at itsivevertex (ivetakes value 1 or 2) is specified by its componentsxtandyt. 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: RequiredVerticesnrv{iv_k}k=1:nrvRequiredEdges (nre{ie_k}k=1:nreThe following features are planed for future work. For periodic boundary conditions, the sectionEquivalencedEdgesindicates that two edges must be meshed the same way: EquivalencedEdgesnee{ie1_kie2_k}k=1:neeCrack definition is the purpose of theCrackedEdgessection. We specify then that an edge is identical in terms of geometry to another edge: CrackedEdgesnce{ie1_kie2_k}k=1:nce

**CREDITS**

Frederic Hecht <Frederic.Hecht@inria.fr> is the author of bamg. Pierre Saramito <Pierre.Saramito@imag.fr> writes this unix man page.

**MORE** **READING**

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