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This paper describes various methods for increasing the computational speed of an existing fatigue solver called PragTic. The paper describes the basic workflow of computational fatigue analysis, including multiaxial fatigue analysis as well. It documents some of the inefficiencies of the original PragTic version, and parallelization and scalability testing of the parallelized PragTic in three different case studies. These studies include a simple model example (hundreds of nodes) and a real world example (millions of nodes). The implemented parallelization techniques are tested using numerical experiments to demonstrate their parallel scalability. As an output of a unique analysis, the number of necessary and feasible evaluated planes in multiaxial analyses is monitored, and the outcome favoring integral methods for the multiaxial fatigue analysis is commented.

The paper investigates strategies for expansion of active set that can be employed by the MPRGP algorithm. The standard MPRGP expansion uses a projected line search in the free gradient direction with a fixed step length. Such a scheme is often too slow to identify the active set, requiring a large number of expansions. We propose to use adaptive step lengths based on the current gradient, which guarantees the decrease of the unconstrained cost function with different gradient-based search directions. Moreover, we also propose expanding the active set by projecting the optimal step for the unconstrained minimization. Numerical experiments demonstrate the benefits (up to 78% decrease in the number of Hessian multiplications) of our expansion step modifications on two benchmarks – contact problem of linear elasticity solved by TFETI and machine learning problems of SVM type, both implemented in PERMON toolbox.

We describe an efficient massively parallel implementation of our variant of the FETI type domain decomposition method called Total FETI with a lumped preconditioner. A special attention is paid to the discussion of several variants of parallelization of the action of the projections to the natural coarse grid and to the effective regularization of the stiffness matrices of the subdomains. Both numerical and parallel scalability of the proposed TFETI method are demonstrated on a 2D elastostatic benchmark up to 314,505,600 unknowns and 4800cores. The results are also important for implementation of scalable algorithms for the solution of nonlinear contact problems of elasticity by TFETI based domain decomposition method.