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ProtoN

A library for fast Prototyping of Numerical methods.

What is this

This is a small library that allows quick and dirty implementations of numerical methods for PDEs.

It started as a throw-away code to implement the cutHHO method (see this paper), however it grew more than expected.

At the moment it implements

  • the 2D version of cutHHO (Fictitious Domain problem)
  • the 2D version of an HHO method for obstacle problems

The library is only 2D and allows only quadrilateral meshes (it had to be quick and dirty, remember?).

Building the code

The code is tested on Mac OS X and on Linux (sorry, I don't have the time to deal with the non-compliance to standards of Windows). To compile you need, apart of a decent C++14 (I'll move to c++17 soon) compiler that should be already available in your system, the following software:

  • CMake
    • brew install cmake on OS X
    • apt-get install cmake on Linux
  • SILO
    • brew install silo on OS X
    • apt-get install libsilo-dev on Linux
  • Lua
    • brew install lua on OS X
    • apt-get install liblua5.3-dev on Linux
  • Eigen3
    • brew install eigen on OS X
    • apt-get install libeigen3-dev on Linux

If you want to just run the code, on OS X, you can tap my homebrew repo with

brew tap datafl4sh/code

and install with just

brew install cuthho

Running the thing

TO BE UPDATED

You will end up with two executables, cuthho_square and convergence_test. The first is the cutHHO driver, the second does a convergence test of the standard cutHHO method.

The executable cuthho_square accepts the following parameters:

  • -M: the number of cells in x direction
  • -N: the number of cells in y direction
  • -k: the degree of the method
  • -m: disable Point Displacement

Be sure to run cuthho_square in a specific directory, because it produces a bunch of files.