The computational TIM technique is devoted to solving time-dependent multidimensional continuum mechanics problems using arbitrarily unstructured Lagrangian grids. The TIM technique allows one to solve 2D problems (TIM-2D) in cylindrical and Cartesian coordinates and 3D problems (TIM-3D) in Cartesian coordinates. To reduce run-times, TIM implements parallelization in a shared memory model using OpenMP interface. Program parallelization is performed by OpenMP parallelization directives added to each loop whose iterations may be independent of each other. Each loop is parallelized independently. Computational modules for gas dynamics, elasticity-plasticity, magnetic hydrodynamics, two-flow and two-temperature behavior, and maintenance of grids, as well as a number of support procedures are parallelized. In some cases we had to revise algorithms used for sequential computations. Parallelization is implemented for computational modules requiring 99% of the total run-time during sequential computations. The algorithms implemented in the code have been verified for a number of test problems and methods runs. The efficiency of computations on eight processors is 85% on average. The paper was prepared on the basis of the authors' report at the International Conference on Parallel Computing Technologies (PaVT-2007; http://agora.guru.ru/pavt2007).

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