Characteristic times in a three scale model with overlapping domain decomposition

A three-scale diffusion model for textiles was given in Goessens et al. (2015): consisting of a fiber, yarn and room model. To analyze and simplify the model, its characteristic times were investigated in Goessens et al. (2015) [8, 9]. At these times the fiber and yarn model, and the yarn and room model, respectively, tend to reach a partial equilibrium concentration. Here an addition will be made to the model based upon the previous work. An overlap zone is considered between the yarn and room level. Then the overlapping domain decomposition technique is used to calculate the exchange of active ingredient from one level to another in this zone. The mass balance for the system with the overlap zone is calculated and tested in C-language.