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1

Varying coefficients in parallel shared-memory variational splitting solvers for non-stationary Maxwell equations

Łoś Marcin, Woźniak Maciej, Paszyński Maciej

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2024

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Vol. 72, nr 3

art. no. e149179

EN

Direction-splitting implicit solvers employ the regular structure of the computational domain augmented with the splitting of the partial differential operator to deliver linear computational cost solvers for time-dependent simulations. The finite difference community originally employed this method to deliver fast solvers for PDE-based formulations. Later, this method was generalized into so-called variational splitting. The tensor product structure of basis functions over regular computational meshes allows us to employ the Kronecker product structure of the matrix and obtain linear computational cost factorization for finite element method simulations. These solvers are traditionally used for fast simulations over the structures preserving the tensor product regularity. Their applications are limited to regular problems and regular model parameters. This paper presents a generalization of the method to deal with non-regular material data in the variational splitting method. Namely, we can vary the material data with test functions to obtain a linear computational cost solver over a tensor product grid with non-regular material data. Furthermore, as described by the Maxwell equations, we show how to incorporate this method into finite element method simulations of non-stationary electromagnetic wave propagation over the human head with material data based on the three-dimensional MRI scan.

2

Three-dimensional simulations of the airborne COVID-19 pathogens using the advection-diffusion model and alternating-directions implicit solver

Łoś Marcin, Woźniak Maciej, Muga Ignacio, Paszynski Maciej

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 4

art. no. e137125

EN

In times of the COVID-19, reliable tools to simulate the airborne pathogens causing the infection are extremely important to enable the testing of various preventive methods. Advection-diffusion simulations can model the propagation of pathogens in the air. We can represent the concentration of pathogens in the air by “contamination” propagating from the source, by the mechanisms of advection (representing air movement) and diffusion (representing the spontaneous propagation of pathogen particles in the air). The three-dimensional time-dependent advection-diffusion equation is difficult to simulate due to the high computational cost and instabilities of the numerical methods. In this paper, we present alternating directions implicit isogeometric analysis simulations of the three-dimensional advection-diffusion equations. We introduce three intermediate time steps, where in the differential operator, we separate the derivatives concerning particular spatial directions. We provide a mathematical analysis of the numerical stability of the method. We show well-posedness of each time step formulation, under the assumption of a particular time step size. We utilize the tensor products of one-dimensional B-spline basis functions over the three-dimensional cube shape domain for the spatial discretization. The alternating direction solver is implemented in C++ and parallelized using the GALOIS framework for multi-core processors. We run the simulations within 120 minutes on a laptop equipped with i7 6700 Q processor 2.6 GHz (8 cores with HT) and 16 GB of RAM.

3

Granulaty bentonitowe jako uszczelnienia mobilnych zapór przeciwpowodziowych

Wrona Piotr, Panna Wojciech, Lipiński Stanisław, Woźniak Maciej

Science, Technology and Innovation

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2020

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Vol. 11, no. 4

16--23

PL

Bentonity i inne surowce smektytowe są szeroko stosowane w wielu gałęziach przemysłu. Autorzy niniejszej pracy dokonali analizy przydatności bentonitowych granulatów pęczniejących w celu ich użycia jako uszczelnień w mobilnych zaporach przeciwpowodziowych. Do tego celu dokonano analizy porównawczej parametrów pęcznienia i uziarnienia trzech dostępnych na rynku granulatów a następnie wykonano próbę makroskopową pęcznienia na specjalnie do tego celu przygotowanym stanowisku badawczym. Wykonane badania wykazały, że nie tylko udział składnika pęczniejącego – smektytu – znacząco wpływa na doszczelnianie układu, ale determinuje go przede wszystkim rozkład wielkości granul i rodzaj smektytu.

EN

Bentonites and other smectite raw materials are widely used in many industries. The authors of the study analyzed the suitability of swelling granulates for their use as a seals in mobile flood barriers. For this purpose, a comparative analysis of the swelling and granulation parameters of three samples available on the market was performed. This results was compared with a macroscopic swelling test, which was realized on the specially prepared test stand. The carried out research shows that not only the content of the swelling minerals – mainly smectite – affect on the sealing of the system, but also they are determine by granules size distribution and the type of smectite.

4

Comparison of multi-frontal and alternating direction parallel hybrid memory iGRM direct solver for non-stationary simulations

Woźniak Maciej, Bukowska Anna

Computer Science

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2020

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T. 21 (4)

419-439

EN

Three-dimensional isogeometric analysis (IGA-FEM) is a modern method for simulation. The idea is to utilize B-splines or NURBS basis functions for both computational domain descriptions and engineering computations. Refined isogeometric analysis (rIGA) employs a mixture of patches of elements with B-spline basis functions and C 0 separators between them. This enables a reduction in the computational cost of direct solvers. Both IGA and rIGA come with challenging sparse matrix structures that are expensive to generate. In this paper, we show a hybrid parallelization method using hybrid-memory parallel machines. The two-level parallelization includes the partitioning of the computational mesh into sub-domains on the first level (MPI) and loop parallelization on the second level (OpenMP). We show that the hybrid parallelization of the integration reduces the contribution of this phase significantly. We compare the multi-frontal solver and alternating direction solver, including the integration and the factorization phases.