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7Multiscale and high.performance computing for multiphysical problems
in a continuous medium)in the case of a gas.dust medium.Theinteraction of dust and gas was taken into account
using the IDIC method [1, 2] within the SPH method used to solve gas.dynamic equations.
An important feature of the work is the use of the open computational package OpenFPM, which makes it
easy to carry out parallel computations. The main advantage of this package is the ready.made (implemented
by the authors of the package) and intuitive, automatically parallelizable vector data structures, the use of
which isidentical both in the case of calculations on a personal computer and in the case of using supercomputer
resources. The paper analyzes the efficiency of parallelization of numerical solutions of the considered
problems.
The research was supported by the Russian Science Foundation grant number 19.71.10026.
References
1. Stoyanovskaya et.al., Two.fluid dusty gas in smoothed particle hydrodynamics: Fast and implicit algorithm for stiff
linear drag // Astronomy and Computing, 2018, V. 25, P. 25.37.
2. Stoyanovskaya et.al., Fast method to simulate dynamics of two.phase medium with intense interaction between
phases by smoothed particle hydrodynamics: Gas.dust mixture with polydisperse particles, linear drag, one.dimensional
tests // J. of Computational Physics, 2021, V. 430.
Numerical solution of a 2d inverse gravimetric problem
D. Kh. Ivanov
Yakutsk branch of Regional Scientific and Educational Center �Far Eastern Center of Mathematical Research�
Email: [email protected]
DOI 10.24412/cl.35065.2021.1.02.80
A 2d inverse gravimetric problem is considered. The aim is to recover the shape of an homogeneous
ore body from the observation of the vertical gravity at the ground surface. To overcome the ill.posedness of
such problem we restrict the unknown body to a star shaped domain. The numerical solution of the direct
problem is based on solving an auxiliary boundary value problem in a bounded computational domain coupled
with the surface integral. According to that, for solution of the inverse problem we present aniterative algorithm
based on conjugate gradient method and specific regularization term. To demonstrate efficiencies of the
proposed method we investigate a modelproblem of a simplified body with the analytical solution and noised
input data.
Edge generalizedmultiscale finite element method for scattering problem in perforateddomain
U. S. Kalachikova1, E. T. Chung2, M. V. Vasilyeva3, Y. R. Efendiev4
1M. K. Ammosov North.Eastern FederalUniversity, Yakutsk
2The Chinese University of Hong Kong (CUHK), Hong Kong SAR
3COIFPM, University of Wyoming, Laramie, WY 82071, USA
4Texas A&M University, College Station, Texas, USA
Email: [email protected]
DOI 10.24412/cl.35065.2021.1.02.81
In this work we consider scattering problem in perforated domain. The mathematical modelis described
by Helmholtz problem related to wave propagation with absorbing boundary condition.For the solution of the
problem using classic finite element method, we construct unstructured fine grid that resolve perforation on
the grid level.Such classic approximations lead to the large system of equations. To reduce size of the discrete
system, we construct a novel multiscale approximation on coarse grid. We use the Edge Generalized
