This paper introduces a novel ray-tracing methodology for various gradient-index materials, particularly plasmas. The proposed approach utilizes adaptive-step Runge–Kutta integration to compute ray trajectories while incorporating an innovative rasterization step for ray energy deposition. By removing the requirement for rays to terminate at cell interfaces – a limitation inherent in earlier cell-confined approaches – the numerical formulation of ray motion becomes independent of specific domain geometries. This facilitates a unified and concise tracing method compatible with all commonly used curvilinear coordinate systems in laser–plasma simulations, which were previously unsupported or prohibitively complex under cell-confined frameworks. Numerical experiments demonstrate the algorithm’s stability and versatility in capturing diverse ray physics across reduced-dimensional planar, cylindrical and spherical coordinate systems. We anticipate that the rasterization-based approach will pave the way for the development of a generalized ray-tracing toolkit applicable to a broad range of fluid simulations and synthetic optical diagnostics.

We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value function of the generalized minimum time problem with discontinuous running cost.

We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the softwareand how new solvers/models can be added to it. A selection of numerical examples are presented.

This essentially numerical study, sets out to investigate various geometrical properties of exact boundary controllability of the waveequation when the control is applied on a part of the boundary. Relationships between the geometry of the domain, the geometry ofthe controlled boundary, the time needed to control and the energy of the control are dealt with. A new norm of the control and anenergetic cost factor are introduced. These quantities enable a detailed appraisal of the numerical solutions obtained and the detectionof trapped rays.