Igor Ostanin

Igor Ostanin, Denis Zorin, Ivan Oseledets

Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches were developed to address the problem of finding optimal design of an engineered structure. Recent works have demonstrated the feasibility of boundary element method as a tool for topological-shape optimization. However, it was noted that the approach has certain drawbacks, and in particular high computational cost of the iterative optimization process. In this short note we suggest ways to address critical limitations of boundary element method as a tool for topological-shape optimization. We validate our approaches by supplementing the existing complex variables boundary element code for elastostatic problems with robust tools for fast topological-shape optimization. The efficiency of the approach is illustrated with a numerical example.

Grigory Drozdov, Igor Ostanin, Ivan Oseledets

We apply the modern technique of approximation of multivariate functions - tensor train cross approximation - to the problem of the description of physical interactions between complex-shaped bodies in a context of computational nanomechanics. In this note we showcase one particular example - van der Waals interactions between two cylindrical bodies - relevant to modeling of carbon nanotube systems. The potential is viewed as a tensor (multidimensional table) which is represented in compact form with the help of tensor train decomposition. The described approach offers a universal solution for the description of van der Waals interactions between complex-shaped nanostructures and can be used within the framework of such systems of mesoscale modeling as recently emerged mesoscopic distinct element method (MDEM).

Igor Ostanin, Ivan Tsybulin, Mikhail Litsarev et al.

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a topological derivative. The numerical solution of the elasticity boundary value problem at every iteration is performed with the boundary element formulation and the kernel-independent fast multipole method. Providing excellent single node performance, scalable parallelization and the best available asymptotic complexity, our method is among the fastest optimization tools available today. The performance of our approach is studied on few illustrative examples, including the optimization of engineered constructions for the minimum compliance and the optimization of the microstructure of a metamaterial for the desired macroscopic tensor of elasticity.

Sahar Pourandi, Igor Ostanin, Thomas Weinhart

Horizontal stirred bed reactors (HSBRs) are used in gas--phase polyolefin production, where efficient solids mixing and controlled residence time distributions are essential for product quality and stability. Despite their industrial relevance, the influence of operating conditions on granular flow and mixing in HSBRs is not well understood. Discrete Element Method (DEM) simulations are used to study the effects of rotation speed and fill level on particle motion, mixing, and axial transport in a lab--scale HSBR. An industrial--grade polypropylene powder is modelled using calibrated contact parameters. Mixing is quantified using the Lacey index in axial (z) and cross--sectional (xy) directions. Particle circulation is characterised via cycle--time analysis and a coarse--grained angular velocity field. Axial dispersion coefficients are obtained from particle trajectories using both Einstein--type and cycle--based approaches, and validated with a diffusion model predicting the axial Lacey index. Results show that axial mixing depends strongly on rotation speed and fill level: higher rotation speeds accelerate homogenization, while higher fill levels slow mixing. Cross--sectional mixing is mainly sensitive to rotation speed, with fill--level effects diminishing at higher speeds. Cycle time decreases with increasing rotation speed and fill level, indicating enhanced circulation. Axial dispersion increases with rotation speed but decreases with fill level, with consistent results across methods. These findings reveal trade--offs between axial mixing, circulation, and dispersion, highlighting the need to balance operating conditions and demonstrating the capability of DEM to support HSBR optimisation.