The Project is devoted to solving the actual problems which has fundamental as well as practical importance in relation with developing new mathematical models of multiphase media for problems of heat-and-mass transfer; with developing the program code complexes for multicore CPU using OpenMP technology and for GPU using CUDA technology. We plan to consider the problems related to forecasting of man-caused and climate impacts on the boundaries of permafrost in Arctic and Subarctic regions on the base of the original approaches used by authors of this Project for simulation of operation of various technical systems for 12 northern oil and gas fields. The novelty of the proposed approaches consists in adaptation of the algorithm to the specific geographical position, taking into account most important climate and man-caused characteristics of considered systems. This approach was used for determining the boundary of thawing of permafrost by a heated well exploited for 3 years; the numerical results coincide with the experimental data with 5% error. For developing the models, we plan to use the data acquired by the field studies for determination of parameters of the nonlinear boundary condition of the soil surface; and by testing of numerical techniques side by side with application of unique analytical approach (the method of special series with recurrent coefficients). For this Project, we also plan to develop 3D nonstationary mathematical model for operation of geothermal open loop systems consisting of several wells including the wells obtained by the method of inclined drilling, determining the perforated portion of the well inside the aquifer (the models usually consider only the perfect wells); to construct the computational grids for complex three-dimensional areas of geothermal reservoir; to develop the parallel algorithms implemented as program complexes for supercomputer for solving the practical problems of designing of geothermal systems. The results of the Project will have scientific importance related to developing of the adequate mathematical models using the data of the field studies for solving the actual problems of developing Arctic regions, as well as the practical interest for companies involved in development and operation of northern oil and gas fields, for climatologists studying permafrost and climate changes. The results of the Project would also be useful for companies involved in design and operation of geothermal aquifers