Feel++

:toc: :toc-placement: preamble :toclevels: 1

The Finite Element Embedded Library in C++

== Gitter Discussion Forum

image:https://badges.gitter.im/Join%20Chat.svg[“Join the chat at”, https://gitter.im/feelpp/feelpp”,link=“https://gitter.im/feelpp/feelpp”]

== Continuous Integration

|=== | Platform & Compiler | master | develop | Travis/Ubuntu & Clang >= 3.5 | image:https://travis-ci.org/feelpp/feelpp.svg?branch=master[“Build Status”, link=”https://travis-ci.org/feelpp/feelpp”] | image:https://travis-ci.org/feelpp/feelpp.svg?branch=develop[“Build Status”, link=”https://travis-ci.org/feelpp/feelpp”] | Buildkite Ubuntu 16.10 |
| image:https://badge.buildkite.com/192023cd78277ebeb80f48580ea813c586ec6dcd0365531b33.svg?branch=develop[“Build Status”, link=”https://buildkite.com/feelpp/feelpp”] |===

== Introduction

link:http://www.feelpp.org[Feel++] is a C++ library for arbitrary order Galerkin methods (e.g. finite and spectral element methods) continuous or discontinuous in 1D 2D and 3D. The objectives of this framework is quite ambitious; ambitions which could be express in various ways such as :

  • the creation of a versatile mathematical kernel solving easily problems using different techniques thus allowing testing and comparing methods, e.g. cG versus dG,
  • the creation of a small and manageable library which shall nevertheless encompass a wide range of numerical methods and techniques,
  • build mathematical software that follows closely the mathematical abstractions associated with partial differential equations (PDE),
  • the creation of a library entirely in C++ allowing to create complex and typically multi-physics applications such as fluid-structure interaction or mass transport in haemodynamic.

Some basic installation procedure are available in the link:INSTALL.md[INSTALL] file, the detailled process is available link:http://www.feelpp.org/docs/develop/BuildingP.html[here].

== Releases

Here are the latest releases of Feel++

== Documentation

== Features

  • 1D 2D and 3D (including high order) geometries and also lower topological dimension 1D(curve) in 2D and 3D or 2D(surface) in 3D
  • continuous and discontinuous arbitrary order Galerkin Methods in 1D, 2D and 3D including finite and spectral element methods
  • domain specific embedded language in C++ for variational formulations
  • interfaced with link:http://www.mcs.anl.gov/petsc/[PETSc] for linear and non-linear solvers
  • seamless parallel computations using PETSc
  • interfaced with link:http://www.grycap.upv.es/slepc/[SLEPc] for large-scale sparse standard and generalized eigenvalue solvers
  • supports link:http://www.geuz.org/gmsh[Gmsh] for mesh generation
  • supports link:http://www.geuz.org/gmsh[Gmsh] for post-processing (including on high order geometries)
  • supports link:http://www.paraview.org[Paraview] and CEI/Ensight for post-processing and the following file formats: ensight gold, gmsh, xdmf

== Examples

=== Laplacian in 2D using P3 Lagrange basis functions

Here is a full example to solve $$-\Delta u = f \mbox{ in } \Omega,\quad u=g \mbox{ on } \partial \Omega$$

[source,cpp]

#include

int main(int argc, char**argv ) { using namespace Feel; Environment env( _argc=argc, _argv=argv, _desc=feel_options(), _about=about(_name=“qs_laplacian”, _author=“Feel++ Consortium”, _email=“[email protected]”));

auto mesh = unitSquare();
auto Vh = Pch<1>( mesh );
auto u = Vh->element();
auto v = Vh->element();

auto l = form1( _test=Vh );
l = integrate(_range=elements(mesh),
              _expr=id(v));

auto a = form2( _trial=Vh, _test=Vh );
a = integrate(_range=elements(mesh),
              _expr=gradt(u)*trans(grad(v)) );
a+=on(_range=boundaryfaces(mesh), _rhs=l, _element=u,
      _expr=constant(0.) );
a.solve(_rhs=l,_solution=u);

auto e = exporter( _mesh=mesh, _name="qs_laplacian" );
e->add( "u", u );
e->save();
return 0;

}

=== Bratu equation in 2D

Here is a full non-linear example - the Bratu equation - to solve $$-\Delta u + e^u = 0 \mbox{ in } \Omega,\quad u=0 \mbox{ on } \partial \Omega$$.

[source,cpp]

#include

inline Feel::po::options_description makeOptions() { Feel::po::options_description bratuoptions( “Bratu problem options” ); bratuoptions.add_options() ( “lambda”, Feel::po::value()->default_value( 1 ), “exp() coefficient value for the Bratu problem” ) ( “penalbc”, Feel::po::value()->default_value( 30 ), “penalisation parameter for the weak boundary conditions” ) ( “hsize”, Feel::po::value()->default_value( 0.1 ), “first h value to start convergence” ) ( “export-matlab”, “export matrix and vectors in matlab” ) ; return bratuoptions.add( Feel::feel_options() ); }

/** * Bratu Problem * * solve \f$ -\Delta u + \lambda \exp(u) = 0, \quad u_\Gamma = 0\f$ on \f$\Omega\f$ */ int main( int argc, char** argv ) {

using namespace Feel;
Environment env( _argc=argc, _argv=argv,
                 _desc=makeOptions(),
                 _about=about(_name="bratu",
                              _author="Christophe Prud'homme",
                              _email="[email protected]"));
auto mesh = unitSquare();
auto Vh = Pch<3>( mesh );
auto u = Vh->element();
auto v = Vh->element();
double penalbc = option(_name="penalbc").as<double>();
double lambda = option(_name="lambda").as<double>();

auto Jacobian = [=](const vector_ptrtype& X, sparse_matrix_ptrtype& J)
    {
        auto a = form2( _test=Vh, _trial=Vh, _matrix=J );
        a = integrate( elements( mesh ), gradt( u )*trans( grad( v ) ) );
        a += integrate( elements( mesh ), lambda*( exp( idv( u ) ) )*idt( u )*id( v ) );
        a += integrate( boundaryfaces( mesh ),
           ( - trans( id( v ) )*( gradt( u )*N() ) - trans( idt( u ) )*( grad( v )*N()  + penalbc*trans( idt( u ) )*id( v )/hFace() ) );
    };
auto Residual = [=](const vector_ptrtype& X, vector_ptrtype& R)
    {
        auto u = Vh->element();
        u = *X;
        auto r = form1( _test=Vh, _vector=R );
        r = integrate( elements( mesh ), gradv( u )*trans( grad( v ) ) );
        r +=  integrate( elements( mesh ),  lambda*exp( idv( u ) )*id( v ) );
        r +=  integrate( boundaryfaces( mesh ),
           ( - trans( id( v ) )*( gradv( u )*N() ) - trans( idv( u ) )*( grad( v )*N() ) + penalbc*trans( idv( u ) )*id( v )/hFace() ) );
    };
u.zero();
backend()->nlSolver()->residual = Residual;
backend()->nlSolver()->jacobian = Jacobian;
backend()->nlSolve( _solution=u );

auto e = exporter( _mesh=mesh );
e->add( "u", u );
e->save();

}

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