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We test four commonly used astrophysical simulation codes; Enzo, Flash, Gadget and Hydra, using a suite of numerical problems with analytic initial and final states. Situations similar to the conditions of these tests, a Sod shock, a Sedov blast and both a static and translating King sphere occur commonly in astrophysics, where the accurate treatment of shocks, sound waves, supernovae explosions and collapsed haloes is a key condition for obtaining reliable validated simulations. We demonstrate that comparable results can be obtained for Lagrangian and Eulerian codes by requiring that approximately one particle exists per grid cell in the region of interest. We conclude that adaptive Eulerian codes, with their ability to place refinements in regions of rapidly changing density, are well suited to problems where physical processes are related to such changes. Lagrangian methods, on the other hand, are well suited to problems where large density contrasts occur and the physics is related to the local density itself rather than the local density gradient.
Dynamic multiobjective optimisation has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of exist
The heart of every Monte Carlo simulation is a source of high quality random numbers and the generator has to be picked carefully. Since the ``Ferrenberg affair it is known to a broad community that statistical tests alone do not suffice to determine
We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on
ODE Test Problems (OTP) is an object-oriented MATLAB package offering a broad range of initial value problems which can be used to test numerical methods such as time integration methods and data assimilation (DA) methods. It includes problems that a
Spectral bounds on the minimum distance of quasi-twisted codes over finite fields are proposed, based on eigenvalues of polynomial matrices and the corresponding eigenspaces. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a way similar t