This paper delves into a rapid and accurate numerical solution for the inverse problem of the nonlinear diffusion equation in the context of multiphase porous media flow. For the realization of this. the combination of the multigrid method with constraint data is utilized and investigated. Additionally. https://pwmhkuzhaojbw.collectblogs.com/79712311/abundancer-a-novel-method-for-estimating-wildlife-abundance-based-on-distance-sampling-and-species-distribution-models