FreeFEM Programs

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Patches

PDF/SVG output by the built-in plot() command

This patch adds PDF and SVG output function to the built-in plot() command, which can generate only PostScript files as default.

This feature has been included in official release of FreeFEM 4.12 or later.

By default in FreeFEM ver 4.12, the compression feature is not supported.
In order to generate compressed PDF files, apply this patch and recompile from sources.

Downloading MUMPS patch for FreeFEM-4.12

In FreeFEM ver 4.12, MUMPS is not correctly downloaded from the specified server when compiling with the --enable-download option.
This patch allows you to download MUMPS from the FreeFEM official site.

Avoiding Segmentation Fault Error of FreeFEM-4.12 on macOS with clang 14.0.3

In macOS 13.3.1 (Ventura) with Apple clang version 14.0.3 (clang-1403.0.22.14.1, for target arm64-apple-darwin22.4.0) provided in CommandLineTools,
both FreeFem++ and FreeFem++-nw cannot be executed due to a segmentation fault error. They might be failed around in the constructor of
struct StackOfPtr2Free in src/fflib/ffstack.hpp.
(After I updated CommandLineTools, I met this error.)

This patch will avoid the error.

PETSc patch

FreeFEM-4.11 automatically downloads/compiles/includes PETSc Ver 3.17.0 by configuration. However, I met an error on Linux (Ubuntu 20.04.3) such as:

/usr/bin/ld: .../FreeFem-sources-4.11/3rdparty/ff-petsc/petsc-3.17.0/fc/lib/libpetsc.so: undefined reference to `GOMP_loop_nonmonotonic_guided_start'
/usr/bin/ld: .../FreeFem-sources-4.11/3rdparty/ff-petsc/petsc-3.17.0/fc/lib/libpetsc.so: undefined reference to `omp_get_max_threads'

• FreeFem-sources-4.11-petsc.patch
• patch application: tar zxf FreeFem-sources-4.11.tar.gz; cd FreeFem-sources-4.11; patch -c -p1 < FreeFem-sources-4.11-petsc.patch
• After executing the configure script, cd 3rdparty/ff-petsc && make petsc-slepc

Dynamic Loading Modules

plotPDF : Save Numerical Solutions/Mesh/Indices to PDF file

As default, FreeFEM uses text file and PostScript to store mesh and numerical results respectively. This module enables us to store them in a single PDF file. Both contours drawing and fill-style output of P0/P1/P1nc/P2 finite elements solutions are available. Meshes are drawn with/without indices (vertex, element, and edge, and boundary labels).

• A major change was made on argument orders (Oct 4, 2022).
• This module has been included in official release of FreeFEM ver.4.12 (or later).
• However, in Windows OS, plotPDF plugin in the pre-compiled packages (FreeFem++-4.12-win64.exe) requires zlib which is not included as system libraries, and plotPDF cannot be loaded by default.
  To enable plotPDF, download plotPDF.dll or zlib123dllx64.zip. For the later, rename zlibwapi.dll to zlib1.dll. plotPDF.dll or zlib1.dll should be placed in the system directory of FreeFEM (C:\Program Files(x86)\FreeFem++ by default).
• document (PDF)
  
• plotPDF-20221011.cpp
• compile: ff-c++ -std=c++11 -DWITH_zlib plotPDF.cpp -lz
• compile (in Windows with MSYS2-x86_64): ff-c++ -static -DWITH_zlib plotPDF.cpp -lz
• install (in Windows): put plotPDF.dll (ver. 2022/Oct/08) into C:\Program Files (x86)\FreeFem++, where you installed FreeFEM.
  (The DLL file is compiled with MSYS2 with zlib. It should be distributed under their licenses.)
• usage:
    bool plotPDF( PDFfilename, mesh Th [, options] );
  bool plotPDF( PDFfilename, mesh Th, Vh u [, options] );
  bool plotPDF( PDFfilename, mesh Th, Vh<complex> u [, options] );
  bool plotPDF( PDFfilename, mesh Th, [Vh u, Vh v] [, options] );
• options
  and plot-PDF-samples.edp

  
  (1) bool plotPDF( PDFfilename, mesh Th [, options] );
      
      Drawing 'mesh Th' only.
  
  (2) bool plotPDF( PDFfilename, mesh Th, Vh u [, options] );
  
      Drawing both 'mesh Th' and 'FE function u'.
  
  (3) bool plotPDF( PDFfilename, mesh Th, Vh u [, options] );
  
      Drawing both 'mesh Th' and 'FE function u'.
  
  (4) bool plotPDF( PDFfilename, mesh Th, [Vh u, Vh v] [, options] );
  
      Drawing both 'mesh Th' and 'FE vector field [u,v]'
  
  Options and Default Values:
  
   --------------------
    page control options
   --------------------
    int size      = 512   : figure pane sizes in pixel
    real ar       = auto  : aspect ratio, x/y
  
    bool meshpage = true  : true if show mesh page
    bool index    = false : true if show mesh with index page
    bool belabel  = false : true if show boundary edge label defined
                             : by "border ... { label=...; }" in .edp
    bool isoline  = true  : true if show isoline of profile
    bool fill     = true  : true if show profile with fill-style
  
   -------------------------
    plot-style control option
   -------------------------
    bool gray        = false : true if monochrome (black white)
    bool bw          = false : (equivalent to gray)
    bool value       = true  : true if show legend in isoline and fill pages
    bool logscale    = false : true if plot functions in logarithmic scale
    real withmesh    = 0.0   : thickness over-layed mesh, 0=white, 1=black
    real fontscale   = 1.0   : ratio of font size for mesh index and belabel
    real[int] viso   = []    : values to plot isolines
    int nbiso        = 12    : number of isolines
    real[int] frange = []    : value range in plotting with fill-style
    int nbfill       = 32    : number of colors (levels) in fill-style
    string fetype    = "P1"  : Finite Element
                             : P0,P1,P2,P1nc(Crouzeix-Raviart) are available
                             : If not specified, piecewise linear interpolated
                             : shape is drawn
    string title             : title of the output PDF file
    string cmm               : comment shown on the graph
    real[int] fmargin = [0,0,0,0] : margin (left, bottom, right, and top)
    int prec         = 3     : number of digits in legends
    real lw          = 1.0   : line width of contour, arrow
    real[int,int] palette    : color spec. for isoline, fill, and vector
                               (default : Color Universal Design ver.4.)
       palette = [ [r0,g0,b0,], [r1,g1,b1], ..., [rN-1,gN-1,bN-1] ];
                   [r0,g0,b0,] => fmin, [r_{N-1},g_{N-1},b_{N-1}] => fmax
       Inteval fmin and fmax is divided into N-1 subintervals, and
       RGB is interpolated in each interval.
  
    If both viso and nbiso are specified, viso is prior to nbiso.
    If fetype="P0", then fill and nbfill are ignored.
  
   -------------------------
    index page
   -------------------------
    bool idcell   = true  : true if show cell (triangle) ID
    bool idvert   = true  : true if show vertex ID
    bool idedge   = false : true if show edge ID
  
   -------------------------
    vector field
   -------------------------
    real ArrowSize   = 1.0 : scale for arrow head size
    real coef        = 1.0 : scale for arrow length
    bool unitarrow   = false : true if draw arrows with same length
  
    * fill is ignored.
  
   -------------------------
    complex-valued function
   -------------------------
    bool zreal = true  : true if show real part
    bool zimag = true  : true if show imaginary part
    bool zabs  = false : true if show modulus (absolue value)
    bool zarg  = false : true if show argument
  
   * fetype is ignored (isoline, fill are interpolated as P1 type).
  
  

plotGnuplot : Save 2D Numerical Solution for gnuplot

A data file which gnuplot can use in 'splot' is generated by this module.

• plotGnuplot-20190315.cpp
• compile: ff-c++ -std=c++11 plotGnuplot.cpp
• usage: bool plotGnuplot( Vh(Th,P1) u, mesh Th, "filename.gpt" );

  
  mesh Th = ...;
  fespace Vh(Th,P1);
  Vh u;
  
  bool ret = plotGnuplot(u, Th, "sample.gpt");
  assert( ret == true );
  
  

• plotGnuplot-sample.edp

Element_CR : Crouzeix-Raviart Element in 2D,3D

Crouzeix-Raviart Element, known as a "non-conforming finite elements". See difference between P1 and CR2d (in 3D-PDF) which is effectively work on Acrobat/Windows.

• Element_CR-20200728.cpp
• compile: ff-c++ -std=c++11 Element_CR.cpp
• usage:

  
  mesh Th = ...;
  load "Element_CR"
  fespace Vh( Th, CR2d );
  Vh u;
  
  mesh3 Th = ...;
  load "Element_CR"
  fespace Vh( Th, CR3d );
  Vh u;
  
  

• Poisson2d_CR.edp, Poisson2d-u-CR.dat.correct
• Poisson2d_CR_gpt.edp
  You can see the results (Poisson2d_CR-triangle.dat.correct and Poisson2d_CR-mpt.dat.correct) via Gnuplot by

  
  gnuplot> plot 'Poisson2d_CR-triangle.dat.correct' w l,'Poisson2d_CR-mpt.dat.correct'
  
  

• Poisson3d_CR.edp, Poisson3d_CR.vtk.correct

SaveHB : Save System of Linear Equations to Harwell-Boeing format

Harwell-Boeing is one of popular formats to store a system linear equations. Since it is available in various software e.g. in Matlab, NAG Library, and SparseLib++, users can use favorite environments in order to solve and to examine properties of linear systems discretized with FreeFEM.

• SaveHB-20180709.cpp (for FreeFem Version 3)
• For Version 4, please see FreeFem-sources-4.*/plugin/seq/SaveHB.cpp
• compile: ff-c++ -std=c++11 SaveHB.cpp
• usage: SaveHB( "filename.hb", matrix A, real[int] b, "title for HB");
  Real Case:

  
  border C(...){...}
  mesh Th=...;
  fespace Vh(Th,...);
  varf vP(u,v)=int2d(Th)(...) + on(C,u=...);
  
  matrix A=vP(Vh,Vh);
  real[int] b=vP(0,Vh);
  
  load "SaveHB"        // without semicolon
  SaveHB("filename.hb", A, b, "Title");
  
  

  Complex Case:

  
  border C(...){...}
  mesh Th=...;
  fespace Vh(Th,...);
  varf vP(u,v)=int2d(Th)(...) + on(C,u=...);
  
  matrix A=vP(Vh,Vh);
  complex[int] b=vP(0,Vh);
  
  load "SaveHB"        // without semicolon
  SaveHB("filename.hb", A, b, "Title");
  
  

• SaveHB-sample.edp, SaveHB-sample-z.edp, SaveHB-README, sample.hb.correct, sample_z.hb.correct

saveMREmotionWebGL : Visualizing Time-harmonic Viscoelastic Wave in WebGL

This module visualizes the time-harmonic viscoelastic wave in a WebGL file with GUI. It is useful for development of MR elastography. Internet connection is required to view on your browsers.

• saveMREmotionWebGL-20230302.cpp
• saveMREmotionWebGL.dll (Module for Windows)
• compile: ff-c++ -std=c++11 saveMREmotionWebGL.cpp
• examples and generated files: mre-nodes.html, mre-motion.html

  
  mesh3 Th3 = ...;
  load "saveMREmotionWebGL"
  saveMREmotionWebGL( "mre-nodes.html", Th3 ); // only output nodes (without motion)
  
  mesh3 Th3 = ...;
  fespace Vh(Th3,P1);
  Vh u1, u2, u3;
  // Solve the time-harmonic 3D viscoelastic equation, whose solutions are (u1,u2,u3)
  
  load "saveMREmotionWebGL"
  saveMREmotionWebGL( "mre-motion", Th3, u1,u2,u3 ); // the suffix ".html" is automatically added
  
  

• usage and options

  
   (1) bool saveMREmotionWebGL( HTMLfilename, mesh Th [, options] );
       
       Drawing vertices used in FEM computation
  
   (2) bool saveMREmotionWebGL( HTMLfilename, mesh Th, 
                Vh u1, Vh u2, Vh u3 [, options] );
   
       Drawing both 'mesh Th' and 'FE function (u1,u2,u3)'.
  
   Options and Default Values:
  
     int nx = DEFAULT_NUM_X : number of nodes in x-direction
     int ny = DEFAULT_NUM_Y : number of nodes in y-direction
     int nz = DEFAULT_NUM_Z : number of nodes in z-direction
  
     real[int] xrange = [ xmin,xmax ] : draw area in x-direction
     real[int] yrange = [ ymin,ymax ] : draw area in y-direction
     real[int] zrange = [ zmin,zmax ] : draw area in z-direction
  
     real[int] radius = [ default,step,min,max ]
     real[int] amp    = [ default,step,min,max ]
     real[int] speed  = [ default,step,min,max ]
     
     bool axis = true : true if show axis
     bool grid = true : true if show xy-grid on z=0 
     real[int] bgcolor = [ 0.8, 0.8, 0.8 ] : background color in RGB
  
     string title : title of the output HTML file
     string cmm   : comment shown on the page
  
  

EDP Files

Shepp-Logan Phantom

• SheppLogan.edp
• Output : SheppLogan2.msh, SheppLogan2.pdf

Boundary Element Methods

• It requires bem.so, plotPDF.so, and ff-mpirun (MPI).
• execution : ff-mpirun -np 1 BEM-Lap2Dinterior.edp -ns -v 0


• 2D interior problem;
  Following results are obtained by line 94 (mesh, contour, and profile)
  


• 2D exterior problem;
  Following results are obtained by line 117 (mesh, contour, and profile)
  


• Scattering problem in 2D exterior domain;
  Following results are obtained by line 100 (real part, imaginary part, and modulus of total wave)