Keywords: distributed memory, GPGPU, parallelisation, simulation, finite element method, tunnelling.

The required accuracy of the simulation results renders the models employed in the simulation of the mechanised shield tunnelling process computationally demanding and large in terms of degrees of freedom. As a consequence, computational methods have to be applied that allow for short turnover times even for very complex simulation models. Here, the most promising approach to increase the computing speed is to apply parallelisation concepts.

The contribution describes three different parallelisation concepts that have been implemented and evaluated in the context of shield tunnelling simulations: parallelisation on shared memory computers using openMP; parallelisation on distributed memory computers using MPI and domain decomposition methods; and massively parallel solving of linear equations on graphics processing units (GPGPU).

The parallel performance of each parallelisation strategy is demonstrated both by means of a simple structural example that employs standard finite element technology from structural mechanics and shield tunnelling examples that feature several non-standard algorithms in the context of finite elements. These encompass spatial search over distributed model domains for the solution of contact problems, multi-physics and multi-phase formulations of soil elements that result in ill-conditioned, non-symmetrical and badly scaled coefficient matrices in the global system equations, and the activation and deactivation of elements in the course of the simulation procedure that results in orphaned nodes in the mesh.

It is shown that for standard structural problems the speedup on distributed memory computers almost reaches the perfect linear speedup for sufficiently large problems. On shared memory computers the parallel performance is boosted by a distributed memory allocation strategy that accounts for the ccNUMA architecture employed in larger shared memory computers. Also for shield tunnelling simulations the speedup that can be achieved on distributed memory computers is reasonably efficient, although the additional complexity of the models requires an additional communication overhead; a fact that decreases the parallel performance to some extent compared to standard finite element technology. It is further shown, that GPGPU implementations of linear solvers are in general a very fast option that outperforms the solution on multi-core CPUs. For the numerically demanding matrices resulting from shield tunnelling problems, however, the performance is significantly lower. This is related to missing heap memory allocation options in current APIs for GPU programming that renders the implementation of effective preconditioners on the graphics processors an open issue for future research.

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