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Many applications and algorithms in the field of gravitational lensing makeuse of meshes with a finite number of nodes to analyze and manipulate data.Specific examples in lensing are astronomical CCD images in general, thereconstruction of density distributions from lensing data, lens-source planemapping or the characterization and interpolation of a point-spread-function.We present a numerical framework to interpolate and differentiate in themesh-free domain, defined by nodes with coordinates that follow no regularpattern. The framework is based on radial basis functions (RBFs) to smoothlyrepresent data around the nodes. We demonstrate the performance of GaussianRBF-based, mesh-free interpolation and differentiation, which reaches thesub-percent level in both cases. We use our newly developed framework totranslate ideas of free-form mass reconstruction from lensing onto themesh-free domain. By reconstructing a simulated mock lens we find that stronglensing only reconstructions achieve < 10% accuracy in the areas where theseconstraints are available but provide poorer results when departing from theseregions. Weak-lensing only reconstructions give < 10% percent accuracy outsidethe strong lensing regime, but cannot resolve the inner core structure of thelens. Once both regimes are combined, accurate reconstructions can be achievedover the full field of view. The reconstruction of a simulated lens, usingconstraints that mimics real observations, yields accurate results in terms ofsurface-mass density, NFW parameter, Einstein radius and magnification maprecovery, encouraging the application of this method to real data.

Mesh-free free-form lensing I: Methodology and application to mass reconstruction