A Direct Discrete Formulation for the Wave Equation

The paper shows how to give a direct discrete formulation of the wave equation starting directly from physical laws, i.e. without passing through differential formulation. Using global variables instead of scalar and vector field functions, a close link between global variables and spatial and temporal elements immediately appears. A preliminary classification of physical variables into three classes, configuration, source and energy variables and the use of two cell complexes, one dual of the other, gives an unambiguous association of global variables to the spatial and temporal elements of the two complexes. Thus one arrives at a discrete formulation of d’Alembert equation on a unstructured mesh.