A dual reciprocity boundary element model for the degradation of strongly eroded archaeological signs

In archaeology, knowledge about the degradation of strongly eroded signs (hieroglyphs) is important to estimate their original shape and thus identify their possible meaning. The degradation of a sign is ruled by a time-dependent flow of material which can be modeled by either a backward or a forward time integration of the governing equations. If the signs alphabet is known, a forward integration scheme is more advantageous because the boundary geometry of a sign can be precisely extracted from the alphabet, allowing to determine a better fit of the integrated shape of a hieroglyph to its present counterpart in the real inscription. The most general governing equation used for the integration scheme is the 2D transient convection–diffusion equation with the upper surface height of hieroglyphs as unknown function. It is numerically integrated by applying the dual reciprocity boundary element method (DRBEM), which allows easy incorporation of different boundary geometries. After designing and implementing a DRBEM degradation model, its calibration is described based on a well-defined hieroglyphic sign still visible in a strongly eroded Hittite inscription. Then the calibrated model is used to identify other hieroglyphs in the same inscription not recognized yet by purely visual means. The results gained so far indicate that strongly degraded signs can be recovered to a certain extent and matched to signs in the existing Hittite alphabet.