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Radiative transfer is a key component in almost all astrophysical andcosmological simulations. We present Magritte: a modern open-source softwarelibrary for 3D radiative transfer. It uses a deterministic ray-tracer andformal solver, i.e. it computes the radiation field by tracing rays through themodel and solving the radiative transfer equation in its second-order formalong a fixed set of rays originating from each point. Magritte can handlestructured and unstructured input meshes, as well as smoothed-particlehydrodynamics (SPH) particle data. In this first paper, we describe thenumerical implementation, semi-analytic tests and cross-code benchmarks for thenon-LTE line radiative transfer module of Magritte. This module uses theradiative transfer solver to self-consistently determine the populations of thequantised energy levels of atoms and molecules using an accelerated Lambdaiteration (ALI) scheme. We compare Magritte with the established radiativetransfer solvers Ratran (1D) and Lime (3D) on the van Zadelhoff benchmark andpresent a first application to a simple Keplerian disc model. Comparing withLime, we conclude that Magritte produces more accurate and more preciseresults, especially at high optical depth, and that it is faster.

Magritte, a modern software library for 3D radiative transfer: I. Non-LTE atomic and molecular line modelling