Mmg3d : User Guide - Institut de Mathématiques de Bordeaux
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1. Vertices np z y 21 refi Tnp Ynp np TC np with np the number of mesh nodes x y zi the coordinates of vertex i and ref its reference an integer NB In dimension 2 it is just y ref Triangles 18 nt 1 2 3 vi v v refi Unt Une Une TE nt with nt the number of mesh triangles v the number of vertex j of triangle i and ref its reference Quadrilaterals nq 1 2 3 4 Uy o Uy v refi 1 2 3 4 Ung Ung Ung Ung refng with nq the number of quadrilaterals vl the number of vertex j of quadrilaterals and ref its reference Tetrahedra ntet 1 2 3 4 vi vi vi v refi 1 2 3 4 Untet Untet Untet Untet refntet with ntet the number of tetrahedra v the number of vertex j of tetrahedron i and ref its reference Hexahedra nh 1 2 3 4 5 6 7 8 Uy V UV V v Vy Vy vy refi 1 72 3 4 15 26 27 8 Unh Unh Unk Unh YUnh Unhr Unh Ynh refan with nh the number of hexahedra v the numver of vertex j of hexahedron i and ref its reference Edges ne el el refi le el Ene Ene re fne with ne the number of boundary edges ele the numbers of the two vertex which compose the edge i and ref its reference SOL file Like MESH format SOL format is composed by keywords describing if the solution is defined on the vertices triangles tetrahedra etc NB On Mmg3d only datas on vertices are taken into account The keywords are the following SolAtVertices SolAtEdges SolAtTriangl2. and or to move all or a part of the domain boundary rigid bodies displacement The software reads a mesh and it is possible to prescribe a map for edges sizes directions and or a displacement vector for the mesh nodes The mesh is then modifying while using local mesh modification of which an insertion procedure based on anisotropic Delaunay kernel NB For the moment only volumic mesh i e the tetrahedra is treated No modification of the surface triangulation made except for the rigid bodies movements and global splitting Mesh adaptation optimization Starting from a mesh and a size direction map the mesh is modified to fit with the prescription The algorithm is decomposed in two parts First the edges lengths are analysed the long edges are cutted and the short are deleted Then when the point density are in agreement with the prescribed size there is a phase of quality optimization edges swaps and point relocation NB In the case where there is no prescribed size we create one with the initial mesh in analysing the edges lenghts Bodies movement When a displacement is prescribed on the initial mesh the final mesh will be such as the surface vertex will be at a new position corresponding with the prescribed displacement This movement can be made with keeping constant the number of nodes but it is not an obligation The final mesh will always be valid in conform meaning NB The surface vertex are moved without ge
3. opts filein mesh out fileout Generic options d Turn on debug mode h Print this message v n Tune level of verbosity m n Set memory size to n Mbytes 0 n Optimization level 1 adaptation 4 use global splitting warning modify boundary mesh 9 moving mesh 10 transform an hexahedral prism mesh in a tetrahedral mesh n turn off optimisation Misc options bucket n Specify the size of bucket per dimension noswap no edge or face flipping nomove no point relocation noinsert no new point out fileout Specify output file name rn n num Specify the number of vertices by box to renumber nodes and the renumberings dt dt to compute the node speed e vn n defined the verbosity level defaulft 3 e mn the integer n defined the allocated memory in Megabytes By default the software allows to generate a mesh with maximum 500 000 points or 3000 000 tetrahedra e mov name gives the displacement filename option 9 see 5 e dt t to compute the node speed option 9 see 5 e in name gives the input filename e out nom gives the output filename e bucket specifies the bucket size default 64 e noswap generate the mesh without applied edge swaps e noinsert generation the mesh in keeping constant the number of nodes no points insertion or edge deletion e nomove generate the mesh without point relocation in optization stage e rn n num this option concerns renumbering s
4. It is also based on keywords but those last are given with numbers The correspondance table betwenn numbers and keywords are given follow Edges Triangles Quadrilat rals Tetrahedra Corners 13 Ridges 14 RequiredVertices 15 RequiredEdges 16 RequiredTriangles 17 15 19 20 Piornal 60 Thus the file must begins with the integer 1 which has been followed by the version number 1 for simple pr cision 2 for double pr cision Next there is the integer 3 Dimension then an integer corresponding to the file position at the end of the infor mation concerning the dimension i e after the integer indicated the dimension so it is the number 20 an integer is stored on 4 bits and including this one we will write five integers then the space dimension 2 or 3 21 The continuation of the file is composed by other keywords with the following convention just after the keyword number you have to indicate the file position at the end of the information concerning this keyword then you give this information Example To write in binary the following mesh MeshVersionFormatted 2 Dimension 3 Vertices ROPOH Fro PRRRO RhReRR Tetrahedra 1 1234 52 End you have to write in binary file the following number 12320341320 0 0 110 1 10 1 1 11 1 1 18123 4 52 54 Explanation 1 MeshVersionFormatted 2 version number 3 Dimension 20 file position at the end of the information concerning the keyword Dimension 4
5. MMG_pMesh mymmgmesh MMG_pTria ptriangle for k 1 k lt mymmgmesh gt nt k 4 ptriangle amp mymmgmesh gt trial k ptriangle gt v 0 num1 ptriangle gt v 1 num2 ptriangle gt v 2 num3 ptriangle gt ref logic NB The node are numbered from 1 to mymmgmesh gt nt in a contiguous way 9 optional If you treat bodies movement initialize the disp structure MMG_pMesh mymmgmesh MMG_pDispl pd for k 1 k lt mymmgmesh gt np k pd amp mesh gt mymmgdisp k pd gt mv 0 depx pd gt mv 1 depy pd gt mv 2 depz 4 4 Metric definition initialization To adapt the mesh according to a metric you must define it in a MMG_Sol structure like that 1 Define a pointer on a Sol structure MMG_pSol sol 2 Allocate this pointer sol MMG_pSol calloc 1 sizeof MMGSol 3 Give the points number sol gt np nbpoint this number is equal to mesh gt np sol gt npmax nbpointmax this number is equal to mesh gt npmax 4 Give the metric type i e isotropic or anisotropic sol gt offset 6 for an anisotropic metric sol gt offset 1 for an isotropic metric 10 5 Allocate the tabular containing the metric field sol gt met doublex calloc sol gt npmax 1 sol gt offset sizeof double sol gt metold double calloc sol gt npmax 1 sol gt offset sizeof double 6 Initialize the met structure that means give on each point the metric values for k 1 k lt mesh
6. Vertices 140 file position at the end of the information concerning the keyword Vertices each vertex is composed by three double precision real and an integer reference and a double precision real is stored on 8 bits thus each vertex information is composed by 8 3 4 28bits There are 4 vertex so 112 bits Then we add the integers for the keyword and the number of vertices 2 4 bits and 20 bits for the previous fields The result is well 140 8 Tetrahedra 168 file position at the end of the information concerning the keyword Tetrahedra each tetrahedron infor mation is composed by 5 integers 54 End 22
7. gt np k isol k 1 sol gt offset 1 for i 0 i lt sol gt offset i sol gt met isol i metrique pointindice_k i 4 5 Out The MMG_pMesh and the MMG_pSol returned by the function are respectively the final mesh and the final metric 5 Bodies movement 5 1 Data input Same as the standard case 3 1 the software reads a mesh format file containing the initial mesh and possibly a sol file containing the metric field To do the mesh movement the software reads a second sol file containing a displacement vector defining on each mesh vertex However only the displacements on boundary vertex are taken into account in Mmg3d 5 2 Options All options are specified on command line See 3 2 5 3 Running In this paragraph we suppose that you have a mesh file named c1 mesh that you would remesh http www math u bordeaux1 fr dobj logiciels data cl mesh a sol file containing the displacement on each mesh vertex dep sol and optionnaly an associated metric named c1 sol http www math u bordeaux1 fr dobj logiciels cl sol To launch the software it is enough to type the following command in terminal window mmg3d 0 9 cube mov dep You will obtain a new mesh which the name will be cube o meshb Remark to obtain an ASCII file you have to specify the output name mmg3d 0 9 cube cube o mesh mov dep To visualize this mesh you could use the software Medit downloadable at the following url http www ann jus
8. the specified metric is ignored the file not containing the same number of points than the mesh file 13 e WARNING INCOMPLETE MESH the software did not have enough memory to generate the mesh thus the final mesh is probably not satured in term of number of nodes However the final mesh is valid so you can rerun Mmg3d beginning with this final mesh by increasing the memory m 500 for instance NB In this case the final mesh is correct in sense of conformity even if it is not well adapted to the prescribed metric 10 Examples 10 1 Mesh adaptation 10 1 1 Uniform metric aligned with axes The metric tensor is diagonal and defined in following way L 0 0 aZh a M P 0 giz 0 0 0 The edges length in the direction x resp y et 2 is ah resp Gh et Oh The initial mesh can be one of them represented on the Figure 1 The Figure 2 shows some volumic cuts on adapted meshes for several a 3 6 values Figure 2 Volumic cut in adapted meshes in the left top a 2 8 1 et y 1 in the right top a 1 P 5 et y 1 onthe bottom a 1 8 1 et y 10 10 1 2 Anisotropic metric The metric is defined by a 3 x 3 symetric positive matrix The Figure 3 shows an example of mesh adaptation where the metric is analytically defined An example of anisotropic adaptation on CFD simulation is represented on the Figure 4 14 Figure 3 Volumic cuts on initial m
9. K on isotropic case is the following 6 y hz h being the length of the edge i of the tetrahedron K and Vx its volume i 1 where hs When an anisotropic metric is defined on each mesh point the quality is more difficult to define In Mmg3d we choose to calculate the tetrahedron quality as its quality measured on the euclidian space relative to an average metric defined on the tetrahedron Lets P Pa P3 Pa the vertex of K The average quality on K is given by the following formula where Mi is the metric at P The following expression give the quality of K on the metric Mmoy njw Y RE Mmo PiP 1 lt i lt j lt 6 a Det M moy Vk NB A such criterion allows to decide if a simplex is a good element You can notice that the quality Q x varies in 1 00 and that more the volume of the tetrahedra is small and more Qg will be high Qk Histogram At the end of the execution Mmg3d prints quality histogram For instance MESH QUALITY 1136 AVERAGE QUALITY 1 4413 BEST ELEMENT QUALITY 1 0767 WORST ELEMENT QUALITY 2 2574 WORST ELEMENT 1183 1125 277 165 114 224 HISTOGRAMM 1 lt 2 2 1130 99 47 2 lt Q lt 3 6 0 53 12 In the previous histogram 1136 number of tetrahedra WORST ELEMENT 1183 1125 1125 is the number of the tetrahedra with the worst quality 7 2 Edges lengths and efficiency index Definition We define an index allowing to quickly judge if the mesh is in agreement with the metric fi
10. MG_pTetra calloc mymmgmesh gt nemax 1 sizeof MMG_Tetra mymmgmesh gt tria MMG_pTria calloc mymmgmesh gt ntmax 1 sizeof MMG_Tria mymmgmesh gt adja int calloc 4 mymmgmesh gt nemax 5 sizeof int mymmgmesh gt disp MMG_pDisp1 calloc mymmgmesh gt npmax 1 sizeof MMG_Displ1 mymmgmesh gt disp gt mv doublex calloc 3x mymmgmesh gt npmax 1 sizeof double mymmgmesh gt disp gt alpha short calloc mymmgmesh gt npmax 1 sizeof short 6 Initialize the point structure that means for all the nodes give the coordinates and the reference MMG_pMesh mymmgmesh MMG_pPoint ppt for k 1 k lt mymmgmesh gt np k ppt amp mymmgmesh gt point k ppt gt c 0 coorx ppt gt c 1 coory ppt gt c 2 coorz ppt gt ref logic NB The node are numbered from 1 to mymmgmesh gt np in a contiguous way 7 Initialize the tetra structure that means for all tetrahedra give the number nodes of the four vertex and the reference MMG_pMesh mymmgmesh MMG_pTetra ptetra for k 1 k lt mymmgmesh gt ne k 4 ptetra amp mymmgmesh gt tetra k ptetra gt v 0 numl ptetra gt v 1 num2 ptetra gt v 2 num3 ptetra gt v 3 num4 ptetra gt ref logic NB The tetrahedra are numbered from 1 to mymmgmesh gt ne in a contiguous way 8 optional Initialize the tria structure that means for all surface triangles dive the node number of the three vertex and the reference
11. Mmg3d User Guide Version 1 0 November 30 2011 Contents 1 Mesh generation by local modifications Isl COME aaee Se eee Ye aS Pe ee RA a be ee ee ERS ee ee 12 AOVERVICW 2d a eGR Ae arg ce tg a a th ed GS ro al ete ee 2 Installation 2 1 Distribution andauthors ws a 4 a ok hh E A Re de da ee Bh ok Os 22 Langages and platforms e iveco ea ee eee EER de de bee ee ha ES 2 3 Compilation and installation cocos See deen eee a Lhd bh oe eS Be adhe Bearers x 20 1 Compilation css 844 44 dew e wh d dat aS at a hn aes od eb obed i began 2 92 Installation 225554 5660 24460688 amp ih ORES Re dsd wee oe BSS A 3 Mesh generation using binary Orb WU oN ies Sesame ys Bec eine acetates wh Se eG et a a e Gop ped ere ene oe eae ea 3 2 Options 2 444 288 8 ob kope r ee AED ae eae ae eee ee hae a a co 3 3 RUNNING e aa p pt A e a oe a ed A a RR ee Se te a eS 4 Mesh generation with library using 4 1 File arguments sore s ssegar ei cd be ARR Re ehh ee ea ee kane eee es AD OPONI s s iaa a aa a eee ba eee eee eee be Ghee Gen Balad OOS wok BE Bo SS Bare ee 4 3 Mesh format sea 0 6d e bh ee KR EDR EE OD e a A ee a 4 4 Metric definition initialization s sa acs ee a a A O EEE eG ws a e e BE ete a E ra ee 5 Bodies movement del Data input 24 se a A e A AAA RA Ded O E a Go ee be Ee eae ee GGG eet ee a eee ae eee Oo DRUMMING sag hoe oe eG GR ee de ara a eae ds Dil Dita Outpt a i a ses s eeSee ee beeen AA awa a alae See eae OOO A aA ww eH 6 Hexa
12. eld Lets note l the length of the edge e in the metric The efficiency index of a mesh is defined as the exponentiel of the mean between the difference with 1 of all the lengths l normalized by the number of mesh edges Lets call 7 this index 1 ne T exp e E5 1 with e l 1 sil lt 1 and e T 1 ifl gt 1 and ne the number of mesh edges i Histogram At the end of the execution the software prints the efficiency index and a length histogram For example RESULTING EDGE LENGTHS 1115 AVERAGE LENGTH 0 9428 SMALLEST EDGE LENGTH 0 5975 172 252 LARGEST EDGE LENGTH 1 5942 215 254 EFFICIENCY INDEX 0 8630 0 71 lt L lt 1 41 1088 97 58 HISTOGRAMM 0 50 lt L lt 0 71 18 1 61 0 71 lt L lt 0 90 554 49 69 0 90 lt L lt 1 11 330 29 60 1 11 lt L lt 1 41 204 18 30 1 41 lt L lt 2 00 9 0 81 In the previous histogram 1115 number of edges 172 252 vertex of the smallest edges 215 254 vertex of the largest edges 8 Mesh visualization To visualize this mesh you could use the software Medit downloadable at the following url http www ann jussieu fr frey logiciels 9 Error and warning The principal errors are the following e NOT FOUND ou UNABLE TO OPEN you have a problem with the input files e INVALID METRIC the specified metric on several points is not a metric the matrix determinant or the eigenval ues are negatives e WARNING WRONG SOLUTION NUMBER IGNORED
13. elegrin scotch If you don t want use SCOTCH you can specify on cmake that you would compile without this library In this case Mmg3d could run more slowly 2 3 2 Installation If you download precompiled version of Mmg3d you just have to unzip it gzip d mmg3d4 0 linux gz 3 Mesh generation using binary 3 1 Input e The input mesh will be to mesh format This format is just composed by one file binary or ASCII for example toto mesh ou toto meshb This file is organised in series of fields identified by key words Besides vertex coordinates and tetrahedra list you can specify other information like faces list corners edges etc Example 1 Example MESH file with triangles and tetrahedra MeshVersionFormatted 2 Dimension 3 Vertices 8 0001 0101 1101 1001 0011 Ot 1d 1111 1011 Triangles 12 14815 12410 327 14 837 12 586 11 256 13 62 1 13 85115 768 11 267 14 438 12 23 4 10 Tetrahedra 6 12842 83272 25862 85212 27682 24382 End Example 2 Example MESH file with quadrilaterals and hexahedra MeshVersionFormatted 2 Dimension 3 Vertices RROOPRROOO0 ORROOHRRO BPrRePrRFOOO 0 PRPPRPRP RPP BE Quadrilaterals 10 11 12 13 14 15 Pwe doen PNNWOAN OONN 0 Y 0100 00H Hexahedra 1 123456782 End The detailled description of this format is made in appendix A An isotropic anisotropic metric can be specify on each input mesh vertices This metric is given in an other file with SOL fo
14. es SolAtQuadrilaterals SolAtTetrahedra SolAtPentahedra SolAtHexahedra SolAtVertices SolAtVertices SolAtEdges 19 SolAtTriangles SolAtQuadrilaterals SolAtTetrahedra SolAtPentahedra SolAtHexahedra Next you have to give the number of entities number of vertex for SolAtVertices number of triangles for SolAtTriangles number of tetrahedra SolAtTetrahedra etc Then you have to indicate the number of solution and the type of each of them 1 for scalar solution 2 for vectorial solution 3 for tensor only symetrical tensor are treated Example 1 scalar solution specifed on mesh vertices MeshVersionFormatted 1 Dimension 3 SolAtVertices 10 1 396303 364391 422417 456066 Jb 5 5 5 10942 257269 O00O0O0O0O0O0O0O0O0O0O0OoOoRre End Example 2 three solutions specified on mesh tetrahedra In this example the first solution is a scalar one one value per tetrahedron the second is a vectorial one two values and the third is a tensorial one three values MeshVersionFormatted 1 Dimension 2 SolAtTetrahedra 5 3123 20 0 396303 0 2 0 3 0 4 0 5 0 7 0 364391 0 2 0 3 0 4 0 5 0 7 0 422417 0 2 0 3 0 4 0 5 0 7 0 456066 0 2 0 3 0 4 0 5 0 7 0 5 0 2 0 3 0 4 0 5 0 7 End Example 3 vectorial solution specifed on mesh vertices MeshVersionFormatted 1 Dimension 3 SolAtVertices oooo orw w o S w co Binary format The MESH and SOL can be written in binary
15. esh and adapted mesh Zoom on anisotropic meshes Figure 4 supersonic flow around an airplane mach 1 6 angle attack 3 degre diameter of the box 1km volumic cut on initial and adapted meshes 15 10 2 Rigid bodies moving Moving object on an uniform mesh The aim of this example is to move horizontaly a car profile on a domain with keeping constant the number of nodes The Figure 5 shows some volumic cuts on the tetrahedral mesh at three differents steps Figure 5 Volumic cuts after one 75 and 150 boundary moves Moving an object on an anisotropic mesh In this example the initial mesh is adapted to an anisotropic metric field The aim is to move two spheres in the domain while keeping the anisotropy On the Figure 6 some volumic cuts are represented Figure 6 Displacement of 2 particles with respect of an anisotropic metric field iteration 0 5 13 16 19 11 FAQ e How can I specify Boundary Conditions that remains untouched by Mmg3d The boundary faces are the Triangles To locate a boundary condition you can put the same reference on a set of triangles This reference will be unchanged by Mmg3d e What must I put like the reference number You can put every number However the new vertex created by Mmg3d will have a reference number equal to zero If there are several reference numbers for tetrahedra Mmg3d will consider several subdomains e Ina mesh with only tetrahedra is it mandatory to specify Edge
16. for debugging node 0 if not bucket size default 64 the possibility to generate the mesh with applied or not edge swaps 1 not authorizing edge swaps the possibilty to generate the mesh in keeping constant the number of nodes no points insertion or edges su pression 1 to keep constant the number of nodes 0 if not the possibilty to generate the mesh with or without point relocation in optimization stage 1 to avoid point relocation 0 if not verbosity level default 3 this integer concerns renumbering stage it allow to tell when renumbering stage appears 0 no renumbering stage 1 renumbering at beginning 2 renumbering after insertion stage 3 default renumbering at the beginning and after insertion stage this integer concerns renumbering stage it is the number of vertices by box default 500 Mesh format To use Mmg3d as a library you must define the informations describing the mesh This informations are specified in a particular structure named Mesh the prototype is in 1ibmmg3d h Details for the structure MMG_Mesh This structure can be decomposed on five parts 1 the general mesh informations number of nodes np and maximal number of nodes which will be generated npmax number of surface triangles nt and maximal number of triangles which could be generated npmax number of tetrahedra ne and maximal number of tetrahedra which could be generated nemax the vertex MMG_pPoi
17. hedra Prisms cutting 6 1 Data put OUIPUE ns s e bm as e E weg ds ae OR RO ee iaa e a ri a i 6 2 Hexahedraxcutting arcs ad Bad od A A he ee ea wae wea A AA ds eee dha iwi hd 6 3 Prims CULTOS a p p 444 EE de a a A A e Se ee ae be S 7 Results evaluation Nel Klements quality 4 006044 4 0 4 20440 esa da ara 7 2 Edges lengths and efficiency index ee ee a 8 Mesh visualization 9 Error and warning 10 Examples 10 1 Mesh adaptation 2 ci sos 0 2244444 wa aaa ES ea a PAA Lea ee ee ee ae a a a 10 1 1 Uniform metric aligned with axes 2 10 1 2 Anisotropic Metric bs is a eda ROG ee ea Ga ae wD bee RE be ee e da Raa 10 2 Rigid bodies Moving a 4 d ws a a BAAD Ow MAL GL VaR RARE SEH aE ERAS ww bv WM 000 w aanw 11 11 11 11 11 11 12 12 12 11 FAQ A Appendix 1 Files format MESH and SOL 17 17 1 Mesh generation by local modifications 1 1 Context The aim of the local mesh methods is to modify iteratively a mesh with local operators points insertion edges supression edge swaps Those methods can be used to refine derefine a mesh improve the elements form quality or control the edges length The local aspect allows to extend them easilly to rigid bodies problems and moving meshes 1 2 Overview Generalities Mmg3d is an anisotropic fully tetrahedral automatic remesher Beginning with a tetrahedral mesh it modifies it iteratively to be in agreement with prescribed sizes and directions
18. nt point This part contains for all the vertex their coordonnates and their logic reference the surface triangles MMG_pTria tria This part contains for all the surface triangles the points number of their three vertex and their logic reference the tetrahedra MMG_pTetra tetra This part contains for all the tetrahedra the points number of their four vertex and their logic reference number of subdomain the displacement prescribed on each vertex in rigid movement case see 5 MMG_pDispl1 disp This part contains a displacement vector for all vertex mesh Definition initialisation of MMGMesh structure to define the MMG_Mesh structure you need to allocate and initialize all the elements described on the previous paragraph The next steps explains how to do that and dive the C code corresponding 1 Define a pointer on a MMG_Mesh structure MMG_pMesh mymmgmesh 2 Allocate this pointer mymmgmesh MMG_pMesh calloc 1 sizeof MMGMesh 3 Give the nodes triangles and tetrahedra numbers of your mesh mymmgmesh gt np nbpoint mymmgmesh gt nt nbtri mymmgmesh gt ne nbtetra 4 Give the nodes triangles tetrahedra maximum numbers mymmgmesh gt npmax nbpointmax mymmgmesh gt ntmax nbtrimax mymmgmesh gt nemax nbtetramax 5 Allocate the structure point tetra tria disp et adja mymmgmesh gt point MMG_pPoint calloc mymmgmesh gt npmax 1 sizeof MMG_Point mymmgmesh gt tetra M
19. ometric checks All quality criterion are based on volumic mesh 2 Installation 2 1 Distribution and authors Mmg3d is written by two authors C cile DOBRZYNSKI IMB Institut Polytechnique de Bordeaux INRIA Bordeaux Sud Duest EPI Bacchus 351 cours de la Lib ration 33405 Talence cedex cecile dobrzynski0math u bordeauxl fr Pascal FREY Laboratoire Jacques Louis Lions Universit Pierre et Marie Curie 4 place Jussieu tour 15 25 75005 Paris frey ann jussieu fr Version 4 0 of Mmg3d is distributed as free libre software under the terms of the GNU GENERAL PUBLIC LICENSE The term of this license is detailled here http www math u bordeaux1 fr dobj logiciels download LICENCE txt You can download the source code of Mmg3d as well as precompiled version on the following website http www math u bordeaux1 fr dobj logiciels download 2 2 Langages and platforms Mmg3d is entirely written in C C89 ANSI norm The current version counts about 55000 lines of source code The code is optionnaly coupled with SCOTCH library and has been tested on all major computer architectures and operating systems 2 3 Compilation and installation 2 3 1 Compilation To easily compile Mmg3d please use cmake tools and refer to the file INSTALL txt Remark By default Mmg3d use the library SCOTCH to renumbering the node and the element of the initial mesh You can download this library on the following website http www labri fr perso p
20. rmat binary or ASCII This file must have the same name as the MESH file with the extension sol for example toto sol or toto solb This file is organised in series of fields identified by key words Example 1 HExample SOL file for isotropic metric MeshVersionFormatted 2 Dimension 3 SolAtVertices O0o00O0O0O0O0O0Oor o 0 RRRRARAR RR q End Example 2 Example SOL file for anisotropic metric MeshVersionFormatted 2 Dimension 3 SolAtVertices 8 13 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 100 0 100 0 O 100 End The detailled description of this format is made in appendix A 3 2 Options All options are given in command line e 0 n with n an integer 0 0 mesh optimization 0 1 mesh generation in agreement with a prescribed metric including points insertion suppression and mesh optimization 0 4 option 1 global splitting warning global splitting involves splitting of boundaries triangles 0 9 rigid bodies displacement and optimization see 5 0 10 transform an hexahedral prism mesh in tetrahedral one see 6 0 1 same as described previously without the optimization phase e d debug mode e h command summary the following message will be written in your xterm MMG3d Release 4 0 c July 20 2010 Copyright c LJLL IMB 2010 Lun 4 avr 2011 11 23 20 CEST usage mmg3d4 0 v n h m n
21. s and Triangles to Mmg3d No you can give only the tetrahedra A Appendix 1 Files format MESH and SOL Mmg3d reads and writes mesh files with MESH format and solutions metric or displacement with SOL format Those files formats allows to read write binary and ASCII files They are composed by one file xx mesh or xx meshb or xx sol or xx solb which contains all needed information for mesh or solution description On the following paragrah we will describe first the ASCII format then the binary one ASCII file The file is organised with key words The comments line must beginning with the character The blank the line return or lt CR gt and the tabs are considered like separators 1 The file must beginning by the keyword MeshVersionFormatted following with the version number This num ber indicates if the file containing single or double precision reals MeshVersionFormatted 1 file writing with simple precision MeshVersionFormatted 2 file writing with double precision 2 The next keyword is about the space dimension Dimension 3 NB the dimension could be equal to 2 but it is not relevant for Mmg3d 3 The file must end by the keyword End File MESH Before the keyword End you have to define all the mesh characteristics vertex elements triangles quadrilaterals tetrahedra hexahedra etc Those entities are defined as follow NB The entities number begins to 1 and not 0 like in C langage
22. sieu fr frey logiciels Remark in the case where there is no metric file the software build one starting from the initial mesh NB if you do not give the file extension mesh b Mmg3d first find the binary file then if there is no mesh b file it tries to open ASCII file In other words if you have in the same directory the files toto mesh and toto meshb and that you type mmg3d 0 n toto the infile will be toto meshb To use the file toto mesh you have to type Mmg3d 0 n toto mesh 5 4 Data output After running you will obtain two files a mesh file containing the new mesh and a sol file 11 6 Hexahedra Prisms cutting 6 1 Data input output The software reads a mesh format file see A containing the initial mesh This mesh can be composed by hexahedra prims and tetrahedra and boundary elements can be composed by triangles and or quadrilaterals After running you will obtain a mesh file containing tetrahedra and triangles 6 2 Hexahedra cutting A majority of hexadra are cutted into six tetrahedra when it is possible The others are subdivised into twelve hedrahedra with adding a vertex at the barycenter of the hexadron 6 3 Prims cutting A majority of hexadra are cutted into three tetrahedra when it is possible The others are subdivised into eight tetrahedra with adding a vertex at the barycenter of the prims 7 Results evaluation 7 1 Elements quality Definition The quality measurement for a tetrahedron
23. tage The integer n is the number of vertices by box by default 500 and num allows to tell when the renumbering stage appears 0 no renumbering stage 1 renumbering at beginning 2 renumbering after insertion stage 3 default renumbering at the beginning and after insertion stage 3 3 Running In this paragraph we suppose that you have a MESH file named cl mesh http www math u bordeaux1 fr dobj logiciels data cl mesh that you would remesh and optionnaly an associ ated metric named cl sol http www math u bordeaux1 fr dobj logiciels data cl sol To launch the software it is enough to type one of the following commands in terminal window mmg3d4 0 0 1 c1 or mmg3d 0 1 in cl You will obtain a new mesh named c1 o meshb and the associated metric named c1 o solb If you would modify the output name mmg3d4 0 0 1 c1 myoutname mesh or mmg3d 0 1 in cube out myoutname mesh In this case you will obtain the two following files myoutname mesh and myoutname sol To visualize this mesh you could use the software Medit downloadable at the following url http www ann jussieu fr frey logiciels Remark in the case where there is no metric file the software build one starting from the initial mesh NB if you do not give the file extension mesh b Mmg3d first find the binary file then if there is no meshb file it tries to open ASCII file In other words if you have in the same directory the files toto mesh and to
24. to meshb and that you type mmg3d 0 1 toto the infile will be toto meshb 4 Mesh generation with library using 4 1 File arguments To use Mmg3d as a library you must include the file Libmmg3d h and call the following C function int MMG_mmg3dlib int opt 7 MMG_pMesh mesh MMG_pSol sol This function takes three arguments 1 a tabular containing nine integers This tabular allows to specify code option see 4 2 2 a pointer on a MMG_Mesh object which contains initial mesh informations see 4 3 3 a pointer on a MMG_sol object which contains metric specification see 4 4 This function returns an integer which is strictly positive if the mesh procedure anormally ended At the end the pointers of MMG_Mesh and MMG_Sol types contain the new mesh and the associated metric 4 2 Options As on the binary using the Mmg3d call is done with options This one must be specified on the tabular int opt 9 This tabular contains 0 4 3 an integer defining the remeshing mode 0 mesh optimization 1 mesh generation in agreement with a prescribed metric including points insertion suppression and mesh optimization 4 option 1 global splitting warning global splitting involves splitting of boundaries triangles 9 rigid bodies displacement and optimization see 5 10 transform an hexahedral prism mesh in tetrahedral one see 6 1 or 4 or 9 same as described previously without the optimization phase debugging mode 1
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