3D and 4D space-time grids for electromagnetic wave computation using finite integration method

A finite integration method on 3D and 4D space-time grids is studied for electromagnetic wave computation, where a non-uniform time-step distribution is naturally introduced. A dual grid based on the Hodge duality and the Lorentz metric is introduced to provide a simple constitutive equation for electromagnetic variables. An improved space-time grid shape is proposed to suppress unphysical wave-reflection.