Welcome to Hermes1D!

Hermes1D is an experimental C++ library for the solution of ordinary differential equations (ODE) and one-dimensional partial differential equations (PDE) with higher-order finite element methods (hp-FEM). In contrast to traditional time-stepping ODE solvers, Hermes1D constructs the solution using a variational principle. It starts from a weak formulation of the ODE/PDE problem and allows the equations to be defined in a very general implicit (vector-valued) form F(y, y', t) = 0. The approximation is a continuous, piecewise-polynomial function defined in the entire interval (0, T). In contrast to time-stepping schemes, the finite element approach makes it possible to prescribe boundary conditions either at the beginning or at the end of the time interval (combinations are possible for systems). The hp-FEM discretization leads to a system of nonlinear algebraic equations that is solved via the Newton's method or JFNK. Sphinx documentation is still in progress. Hermes1D comes with a free interactive online lab powered by UNR HPC cluster.

Hermes1D is distributed under the BSD license (it covers all files in the Hermes1D repository unless stated otherwise.), see the LICENSE file for a copyright/license information and the AUTHORS file for the list of authors.

Copyright (c) 2009 hp-FEM group at the University of Nevada, Reno (UNR). Email: [email protected], home page: http://hpfem.org/.

Compilation

Install the required libraries first. If you are using a Debian-based system, do:

$ apt-get install cmake g++

$ cmake . $ make

Examples

$ cd examples/laplace $ ./laplace $ gnuplot gnuplot> plot './solution.gp' w l

Documentation

Install the required libraries first, if you are using a Debian-based system, do:

$ apt-get install python-sphinx

then:

$ cd doc $ make html $ firefox _build/html/index.html

Python

python -c 'print "set(WITH_PYTHON yes) "' > CMake.vars cmake . make cd examples/schroedinger ./schroedinger