GridRipper

This is a fourth order precision Adaptive Mesh Refinement (AMR) code for solving hyperbolic systems of partial differential equations (PDE-s) numerically. This package, the GridRipper, is the core library of numerical methods. Concrete implementation of PDE-s can be done in its application package GridRipperApp.

A physical model consists of a partial differential equation (PDE) and an initial condition, both implemented as C++ classes in the GridRipperApp package. This application library is linked against the GridRipper core library, forming a PDE solver program after the build phase. Parameters for the PDE solver program can be specified in an input file. Valid input files for already implemented PDE-s are found within the GridRipperApp package. The input file can also contain certain function formulae, interpreted by a formula parser, hence it is possible to specify simple initial conditions without writing program code.

Simulation parameters specified in an input file:

Physics: model and parameters
Basic simulation parameters:
- Base grid resolution and maximum number of refinement levels.
- The Courant factor. It can be constant or a function of time.
- Integration method: RK2, RK4, Iterated Crank-Nicholson or Lax-Wendroff.
- The σ factor of the numerical dissipation term. It can be coordinate dependent.
Special mesh refinement related parameters:
- Error function and error tolerance for the refinement condition.
- Frequency of error checking.
- Maximum number of time steps without regridding.
- Buffer zone size.
Output:
- Time difference for datafile writing.
- ...

API documentation

GridRipper/C++ API
See also 'man gridripper' after installation for practical instructions.

Tools

Some of the below tools are shipped with the GridRipper core library, some of them are on the other hand are generated when building and installing GridRipperApp application package of GridRipper.

gridripper	Solves the system of PDEs numerically, stores the solution in a binary file (.bdata).	(C++)
grr-odeshoot	Solves an ODE with shooting method.	(C++)
grr-intdx	Reads bdata, numerically integrates the specified function(s) in space using a fifth order polynomial approximation.	(C++)
grr-curves	Reads bdata and creates curves by calculating the x-intercepts of the specified function.	(C++)
grr-datatable	Reads the input and the bdata files, prints the values of the specified field components and grid functions in text format.	(C++)
grr-bdata2txt	Reads bdata and prints its contents in text format. Note that it cannot print functions of field components, use grr-datatable for that.	(Perl)
grr-meshdensity	Reads bdata, prints mesh refinement info.	(Perl)

Applications

The main aim for developing the code was to solve the Einstein equations numerically. The following problems are currently investigated:

Gravitational collapse of fluid or scalar field in spherical symmetry.
Creation of baby universes.
Cosmic inflation.
Einstein-Klein-Gordon system in 3D scenarios using multipole expansion.

Download

The GridRipper core library source: gridripper.tar.gz.
The GridRipperApp application package source: gridripperapp.tar.gz.

First, download, build and install the GridRipper core library. Then download, build and install the GridRipperApp application package source. To write your own PDE, you can simply extend the GridRipperApp code with your equation.

Authors and contributors

Péter Csizmadia — C++: AMR algorithm
András László — C++: multipole methods
István Rácz — ideas and theoretical background

Please contact us if you would like to join to the developers. Our e-mail addresses are found in the manual pages shipped with the GridRipper and GridRipperApp source packages (see the 'man' directory of the above downloadable source packages).

Thanks

This work was supported in part by OTKA grant K67942.

References

P. Csizmadia, Testing a new mesh refinement code in the evolution of a spherically symmetric Klein-Gordon field, International Journal of Modern Physics D15 (2006) 107-119 [arXiv:hep-th/0505036]
P. Csizmadia, Fourth order AMR and nonlinear dynamical systems in compactified space, Classical and Quantum Gravity 24 (2007) S369-S379.
P. Csizmadia, A. László, I. Rácz, Linear waves on fixed Kerr background and their relevance in jet formation, Journal of Physics: Conference Series 218 (2010) 012007.
P. Csizmadia, A. László, I. Rácz, On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance, Classical and Quantum Gravity 30 (2012) 015010.

28 January 2011, A. László