  We introduce a new code, ECOSMOG, to run N-body simulations for a wide class
of modified gravity and dynamical dark energy theories. These theories
generally have one or more new dynamical degrees of freedom, the dynamics of
which are governed by their (usually rather nonlinear) equations of motion.
Solving these non-linear equations has been a great challenge in cosmology. Our
code is based on the RAMSES code, which solves the Poisson equation on
adaptively refined meshes to gain high resolutions in the high-density regions.
We have added a solver for the extra degree(s) of freedom and performed
numerous tests for the f(R) gravity model as an example to show its
reliability. We find that much higher efficiency could be achieved compared
with other existing mesh/grid-based codes thanks to two new features of the
present code: (1) the efficient parallelisation and (2) the usage of the
multigrid relaxation to solve the extra equation(s) on both the regular domain
grid and refinements, giving much faster convergence even under much more
stringent convergence criteria. This code is designed for performing
high-accuracy, high-resolution and large-volume cosmological simulations for
modified gravity and general dark energy theories, which can be utilised to
test gravity and the dark energy hypothesis using the upcoming and future deep
and high-resolution galaxy surveys.
