Development of a Godunov method for Maxwell's equations with Adaptive Mesh Refinement

• A Godunov method is used to solve a conservative law's form of Maxwell's equations.
• Suitable interpolation schemes and limiters allow solving Maxwell's equations with AMR.
• A new numerical method for boundary conditions allows to simulate unbounded domains.
• Using AMR allows solving big domain simulations in reasonable computational time.

In this paper we present a second order 3D method for Maxwell's equations based on a Godunov scheme with Adaptive Mesh Refinement (AMR). In order to achieve it, we apply a limiter which better preserves extrema and boundary conditions based on a characteristic fields decomposition. Despite being more complex, simplifications in the boundary conditions make the resulting method competitive in computer time consumption and accuracy compared to FDTD. AMR allows us to simulate systems with a sharp step in material properties with negligible rebounds and also large domains with accuracy in small wavelengths.

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