Keywords: coupled problem, nonstationary flow, nonstationary solver.

This article deals with numerical solution of coupled problems. In contrary to pure mechanical problems, there are several difficulties which require special attention. Systems of algebraic equations arising from coupled problems are generally nonlinear and matrices of such systems are nonsymmetric and indefinite. Big differences in exponents of matrix entries lead to serious numerical troubles during solution of system. Our first experiences with solution of complicated coupled problems are mentioned in this article.

Assessment of durability and serviceability of nuclear power plants is actual problem in many countries. The most important part of power plant is reactor containment which is made from concrete with or without steel lining. There are several requirements on the reactor containment. Basically, it must protect reactor from external effects and also external environment from an eventual accident. Mechanical analysis is used for the limit state assessment and transport analysis is used for description of leakage of pollutant to the external environment. Eventual accidents can lead to large pressure inside of the reactor containment, which can cause damage of the concrete and therefore it has impact on transport processes of pollutants. Therefore coupled hydro-thermo-mechanical analysis is required for correct assessment of reactor containment properties.

Hydro-thermo-mechanical problems are extremely complicated due to many nonlinearities and therefore only numerical methods are used for two and threedimensional problems. One of the suitable methods is the finite element method where each node has 6 degrees of freedom in threedimensional problems (3 displacements, temperature and 2 pore pressures). System of linear algebraic equations (after discretization and linearization) contains many unknowns and appropriate solver must be used. Sequential computer codes have severe difficulties with memory and CPU time in connection with such systems. Therefore parallel computers are used still more often in complicated analysis. Probably the most powerful tool for solution of large systems of equations with help of parallel computers is the family of domain decomposition methods.

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