A class of multivariable systems is considered where modeling and control problems related to real physical processes can be solved only using approximate computational approach. The simulation processes are defined as solving mesh (finite-difference and finite-element) approximations of initial-boundary problems corresponding to original equations of mathematical physics for proper physical processes. The high dimensionality issues arising in the frame of such approach are overcome by means of decomposition and partitioning combined
with multigrid spatial versions of approximating operator equations in function spaces. Multilevel computational methods for modeling and solving optimal control problems are oriented to using multiprocessor computer systems with parallel computing in message passing interface environment. The proposed results are actual both in theoretical and applied aspects. For instance, using the proposed approach to resolving problems of natural hydrocarbon deposit
development simulation and optimal control opens wide capabilities for choosing efficient strategic decisions