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The paper deals with the solution of large multibody contact problems using massively parallel computers and domain decomposition methods. These methods can solve the problems discretized by billions of nodal variables at the cost nearly proportional to the number of variables using up to thousands cores before the communication costs start to dominate the computational costs. The paper describes the ingredients essential for efficient massively parallel implementation that increases the parallel scalability beyond the limit mentioned above. The improvements were enhanced into a new software package PERMON which is based on PETSc. The performance of the algorithm is demonstrated on the solution of an academic benchmark discretized by nearlybillion of nodal variables.

Detections of material regions on CT-scans of solids are commonly treated manually by an expert. Although such manual detections have many advantages, some amount of human error is also incorporated. Moreover, expert opinions may vary significantly. We present an application of the k-means++ clustering as an alternative option to manual way of material area detections. k-means++ clustering is derived from k-means (the method of vector quantization, originally from signal processing), popular for cluster analysis in data mining and image processing communities. The algorithm s main advantages are its simple implementation and fast convergence to a local optimum of an objective function. We benchmark the suggested approach on transverse CT-scans of a fibre-reinforced concrete solid. Moreover, we introduce a technique for processing air distribution, such that the appropriate pixels detected as the pixels of air are converted into pixels representing concrete. The technique is based on the connected component algorithm. Benchmark and results of proposed method conclude the paper.

The final step in the solution of contact problems of elasticity by FETI-based domain decomposition methods is the reconstruction of displacements corresponding to the Lagrange multipliers for ''gluing'' of subdomains and non-penetration conditions. The rigid body component of the displacements is usually obtained by means of a well known but quite complex formula, the application of which requires reassembling and factorization of some large matrices. Here we propose a simple formula which is applicable to many variants of the FETI based algorithms for contact problems. The method takes a negligible time and avoids reassembling or factorization of any matrices.