Comparison of the effectiveness of methods for solving systems of linear equations in the problem of modeling the contact interaction of fuel elements in a thermoelastic formulation

Various algorithms for solving systems of linear algebraic equations that arise when modeling problems of contact interaction of thermoelastic bodies with a changing configuration of the contact surface are considered. The implementations of modified iterative methods, the Uzawa method, as well as algorithms based on the use of the Gauss method and the generalized method of minimal residuals (GMRES) with two iterative refinement options allowing for the exit from contact of individual sections of the contact boundary are presented. The efficiency of the presented algorithms is compared in relation to a problem simulating thermomechanical processes in a section of a fuel element that includes up to 100 fuel pellets.