GridRipper

A fourth order precision Adaptive Mesh Refinement (AMR) code for solving hyperbolic systems of partial differential equations numerically.

A physical model consists of a partial differential equation (PDE) and an initial condition, both implemented as C++/Java classes. Parameters can be specified in the input file. The input file can also contain function definitions, hence it is possible to specify initial conditions without writing program code.

Simulation parameters:

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

Tools

gridripper	Solves the system of PDEs numerically, stores the solution in a binary file (.bdata).	(C++)
jgridripper	(Same for models implemented in Java.)	(Java)
xgridripper	GridRipper GUI, simulation with graphical monitoring.	(Java)
grr-odeshoot	Solves an ODE with shooting method.	(C++)
grr-jodeshoot	(Same for ODEs implemented in Java.)	(Java)
grr-joderelax	Solves an ODE with relaxation method.	(Java)
grr-intdx	Reads bdata, numerically integrates the specified function(s) in space using a fifth order polynomial approximation.	(C++)
grr-jintdx	(Same for models implemented in Java.)	(Java)
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-jdatatable	(Same for models implemented in Java.)	(Java)
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)
grr-calc	Calculator; useful for testing expression evaluation.	(C++)
grr-jcalc	(Same in Java.)	(Java)

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

Not yet available, first the core library should be separated from models.

Authors and contributors

Péter Csizmadia — C++, Java
András László — C++: multipole, incremental integration
István Rácz — ideas and theoretical background

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.

17 June 2009, P. Csizmadia