The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for numerical relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust three-dimensional calculations. The potential of the resulting numerical code is demonstrated by using black hole space-times as a test bed. The evolution of a Schwarzschild black hole can be followed up to times greater than one hundred black hole masses. A distorted black hole is also modeled from the Misner double black hole initial data, the two holes being surrounded by a single horizon.

In the interior of neutron stars, the induction equation regulates the long-term evolution of the magnetic fields by means of resistivity, Hall dynamics and ambipolar diffusion. Despite the apparent simplicity and compactness of the equation, the dynamics it describes is not trivial and its understanding relies on accurate numerical simulations. While a few works in 2D have reached a mature stage and a consensus on the general dynamics at least for some simple initial data, only few attempts have been performed in 3D, due to the computational costs and the need for a proper numerical treatment of the intrinsic non-linearity of the equation.Here, we carefully analyze the general induction equation, studying its characteristic structure, and we present a new Cartesian 3D code, generated by the user-friendly, publicly available Simflowny platform. The code uses high-order numerical schemes for the time and spatial discretization, and relies on the highly-scalable SAMRAI architecture for the adaptive mesh refinement. We present the application of the code to several benchmark tests, showing the high order of convergence and accuracy achieved and the capabilities in terms of magnetic shock resolution and three-dimensionality. This paper paves the way for the applications to a realistic, 3D long-term evolution of neutron stars interior and, possibly, of other astrophysical sources.

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Simflowny is an open platform which automatically generates parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support an extended set of families of models, in particular: i) a new generic family for partial differential equations, which can include spatial derivatives of any order, ii) a new family for agent based models to study complex phenomena -either on a spatial domain or on a graph-. Additionally we introduce a flexible graphical user interface (GUI) to accommodate these and future families of equations. This paper describes the new GUI architecture and summarizes the formal representation and implementation of these new families, providing several validation results. PROGRAM SUMMARYProgram Title: Simflowny Licensing provisions: Apache License, 2.0 Programming language: Java, C++ and JavaScript Journal Reference of previous version: Comput. Phys.