Conference Program: Abstracts

Existence theory and generation method for structured meshes based on Abel-Jacobi theory

Na Lei, Xiaopeng Zheng, Yiming Zhu, Wei Chen, Zhongxuan Luo, Xianfeng Gu
Dalian University of Technology

Abstract: Structured meshes play crucial roles in engineering fields. This work studies the configurations of singular vertices on structured meshes based on Abel-Jacobi theory. It discovers the fundamental relations between the structured meshes and the meromorphic differentials, and give a unified, simpler proof for the non-existence of some structured meshes with special singularities and coloring schemes. This work further proposes a general algorithm for structured mesh generation which can produce the most conformal structured quad meshes, triangle mesh and hexagon meshes. Experiment results demonstrate the efficacy and efficiency of our algorithm.

Parametrization of 2D complex regions using UNAMalla 6: a block structured mesh generator

Pablo Barrera, Iván Méndez Cruz
Universidad Nacional Autónoma de México

Abstract: A method for the construction of parametrizations of simply connected regions is extended to polygonal regions with holes. It decomposes complex regions into simply connected subregions suitable for structured mesh generation. The parametrizations are block structured quad meshes. The method is implemented in a new version of our mesh generator UNAMalla 6. High quality meshes on complex regions can be generated using this meshing software.

http://tikhonov.fciencias.unam.mx/unamalla

Mesh untangling and barrier variational mesh optimization: from ideas to the engineering practice. In memory of S.A. Ivanenko (1953–2003), co-founder of the NUMGRID conference.

Vladimir Garanzha
Dorodnicyn Computing Center

Abstract: In 1988 Sergei Ivanenko was surprised by the fact that the standard finite element approximation of the Winslow functional (Dirichlet functional for the inverse mapping) provides an infinite barrier on the set of nondegenerate quad meshes. From this observation he made two immediate conclusions: (a) mesh optimization inside the admissible set guarantees that all elements remain valid and (b) one needs a certain continuation procedure (mesh untangling) to build admissible mesh from an arbitrary initial state. Now, both these statements look commonplace but more that 30 years ago it was considered somewhat like a marginal activity. Inventing algorithms which are order of magnitude slower compared to existing elliptic mesh smoothers was considered to be a ridiculous idea. In 1988 Ivanenko published two papers in the Soviet Computational Mathematics and Mathematical Physics journal. The first one, jointly with A. Charakhchyan, presented the idea of a barrier method, while another one introduced the concept of untangling and the idea that untangling should be attained in a finite number of steps. The second paper, surprisingly, was not included into the modern citation indexes and remains largely unknown outside of Russia.

In 2001 Ivanenko, jointly with V. Garanzha, founded NUMGRID as a meshing minisymposium in St. Petersburg. In 2002, twenty years ago, NUMGRID was launched as an independent conference which was Ivanenko’s first and last NUMGRID meeting before his untimely death.

Currently, Ivanenko’s ideas became mainstream. Multiple papers on the topic are published in the leading journals and conference proceedings. Mesh untangling and barrier methods are now integrated into industrial software.

In this talk we show how the barrier method can be used to build deformations of lowest distortion using the quasi-isometric stiffening (QIS) technique and show its relation to de Boor equidistribution principle. Finite number of steps theorems are eventually proved for mesh untangling and for least distortion deformation problem. We show that the resulting algorithm provides best results on a huge international 2d/3d untangling/deformation datasets both in terms of robustness of untangling and worst quality of resulting deformation.

Splice topology-based quadrangulation for partitioned patches

Jiguang Lian, Haisheng Li, Xiaoqun Wu, Nan Li
Beijing Technology and Business University

Abstract: Surface structured mesh generation is an important part in Computational Fluid Dynamics (CFD) preprocessing stage. The traditional method cannot automatically divide the 3D surface topology at complex structures. Thus, we propose a mesh feature-based block segmentation method for surface structured mesh generation. The core idea is to segment the complex 3D model into several simple parts, and map each part to the 2D parametric domain. Then, we perform topology division and structured mesh generation in the parametric domain. Finally, we splice each part accurately according to the structured mesh feature distribution. To ensure the mesh topology is consistent when splicing surface structured mesh, we also improve the parameterization algorithm. In order to demonstrate the efficiency and effectiveness of the proposed method, some surface structured mesh generation examples and comparison with previous methods are presented.

Surface structured mesh generation system based on symmetry preserving parameterization

Haoxuan Zhang, Haisheng Li, Peng Wang, Nan Li
Beijing Technology and Business University

Abstract: The purpose of the parameterization is to map the model surface from 3D space to 2D parametric domain space. However, the traditional algorithm cannot guarantee the symmetry of the original model. We propose a symmetry preserving parameterization algorithm. We use plane reflection symmetry transformation to solve the main symmetry plane of the model and calculate the symmetry factor. Based on the fixed points of the free boundary and the symmetry factor, a conformal parametric symmetry plane is obtained. We also build a surface structured mesh generation system based on algorithm pipeline. Experimental results show that the proposed algorithm can get high quality results and almost automatic.

Local invertibility of global parameterizations for quad mesh generation

Nicolas Ray, Dmitry Sokolov, Vladimir Garanzha
Université de Lorraine

Abstract: An important application of parameterizations is the generation of quad meshes. Given a 3D surface and its 2D flattening, applying the inverse of the map to a 2D grid generates a grid on the surface, i.e. a quad mesh. Naturally, this technique requires the map to be locally invertibile, hence the importance of the untangling approach.

Texture space optimization via harmonic map

Wei Chen, Yuxue Ren, Na Lei, Zhongxuan Luo, Xianfeng Gu
Dalian University of Technology

Abstract: Texture mapping is a common technology in the area of computer graphics, it maps the 3D surface space onto the 2D texture space. However, the loose texture space will reduce the efficiency of data storage and GPU memory addressing in the rendering process. Many of the existing methods focus on repacking given textures, but they still suffer from high computational cost and hardly produce a wholly tight texture space. In this paper, we propose a method to optimize the texture space and produce a new texture mapping which is compact based on harmonic map. The proposed method is computationally robust and efficient. Experiments show the effectiveness of the proposed method and the potency in improving the storage and rendering efficiency.

Coordinate transformations and numerical grids for solving problems with hybrid layers

Vladimir Liseikin, Samir Karasuljic, Viktor Paasonen
FRC ICT SB RAS

Abstract: The paper describes an explicit approach for generating layer–damping coordinate transformations and corresponding layer– resolving grids for problems having hybrid-type layers. The grids are generated on the basis of qualitative estimates of solution derivatives in the layers of one-dimensional problems with a turning point and a small parameter in the coefficient affecting the second derivative. The paper presents results of numerical experiments, using appropriate coordinate transformations and layer– resolving grids, for two-point boundary-value problems and two–dimensional Navie–Stokes equations modelling a viscous fluid flow in a cavern.

The problems of mesh generation, processing, and filtering in the areas of mixed reality

Denis Shchepetov
Huawei

Abstract: Mixed (Augmented and Virtual) reality is a young area of knowledge with its own features, filled with young cheerful people with their own established vocabulary. The cheerfulness of research grows as interest in mixed reality is substantial and growing. From the content producers’ point of view, the content must be responsive, realistic, and fit into the surrounding landscape. Particularly, for those who were involved in CAD and accurate physical simulations, this means that what they did on supercomputers and in a good manner, they should do on user devices and fast. For those who will work in the area of augmented reality, this means that objects that were once virtual now should behave like real ones – reflect light, cast shadows, be drawn in realtime, and interact with the user with all the details of their shape. For those who work in the areas of virtual reality this means, at least, that the objects captured using photogrammetry should look no worse than those developed by a professional designer.

These are the problems that have already shown themself or are arising now with clear contours. For most of these problems, grid / mesh generation, processing, and refinement are “the root of the evil”. The report will be dedicated to the description of these problems and give an overview of the existing methods for the sake of the auditory preparation for this new evil.

More precisely, the following questions are considered:

  1. Cloth simulation and its sensitivity to cloth mesh parameters, as well as the influence of different mesh refinement algorithms on the quality of cloth simulation.
  2. For the 4d video, evaluation of current methods for generation of “time-consistent” meshes from the point clouds. The complexity and drawbacks of the existing approaches will be shown.
  3. Mesh simplification and building problem will be evaluated altogether with modern deep learning approaches in the areas of simulation of signal propagation for a new 5G environment.
  4. And (as the final part) a small problem of navigation of self-driving cars in a flat world will be considered as well as the difficulties that one could suffer while designing such an algorithm.

XField: an algorithmic pipeline framework for grid data visualization

Xiang Su, Nan Li, Ya Chen, Zhiyong Guan, Tao Feng
Beijing Technology and Business University

Abstract: This paper presents a new framework for visualizing grid data based on pipeline mechanism, XField. It is applied to the scientific visualization of complex grid data onto CFD flow field numerical simulation tasks. By deploying a post-processing algorithm engine to ensure the processing and analysis of complex grid data; using a mechanism based on multi-pipeline fusion, data adapters are used to realize the data exchange of multiple algorithm pipelines, and by deploying a visualization rendering engine based on UE4 to ensure the visual effect and artistic expression of complex data. Taking the numerical simulation of waverider as an example, the application of the algorithmic pipeline built by grid generation and its visualization, digital geometry processing, grid multi-physics data visualization and digital twin scenario on this framework is described respectively to verify the usability and flexibility of the framework.The application of blast furnace production lines and wind tunnel experiments on the framework are also demonstrated to have verified the scalability of the framework.

Challenges and opportunities for CAD/CAM/CAE research

Alexander Malyshev
Huawei

Abstract: Engineering areas such as CAD, CAM and CAE have been under active research for 70 years. Historically being practical, they are still focused on practical aspects. Academia pursues goals like novelty or publications number. Industry looks for robustness. This talk highlights discrepancies between academia and industry from the latter’s point of view. Experience of handling these issues is given and generalized as potential way out from academia-industry’s dead end.

Adaptive refinement of tetrahedral meshes in electromagnetic simulation

Aleksandr Chikitkin, Nikita Aseev, Evgeniy Pesnya
Huawei

Abstract: We consider different aspects of adaptive mesh refinement in electromagnetic simulation of different structures. Quality of adaptive refinement is of great importance for finite element solution of Maxwell equations. Input data at each iteration of refinement are current mesh and error indicators for each element computed using a posteriori error estimates. In this report we compare different variants of how this information can be used for refinement of mesh elements. Examples of meshes obtained by different approaches are presented.

Electromagnetic Finite Element analysis based on adaptive mesh method

Jiaxin Zhao, Qi Yang, Yu Wang, Jun-fei Zhang
Zwsoft Co. Ltd.

Abstract: In electromagnetic finite element analysis, meshing is one of the key technologies affecting simulation accuracy and computational efficiency. In this paper, the adaptive mesh method based on the a posteriori error of the simulation is used to realize the automatic meshing and automatic optimization. First, the electromagnetic finite element analysis is performed based on the initial mesh, and then, according to the simulation results of the current mesh, we calculate the a posteriori error and build the metric tensor field. The topological optimization mesh generator can automatically construct the optimized mesh with the help of the metric tensor field. The mesh size will be reduced in the larger error area to improve the simulation accuracy, and the mesh size may be increased in the smaller error area to improve the calculation efficiency. Finally, the simulation is performed again based on the adapted mesh, and iteratively optimized until the a posteriori error converges. This method can reduce the difficulty of pre-processing and obtain more accurate results.

XaaS (X as a service) via industry software cloud

Frank (Zhigang) Fang, Yong Yuan
Huawei

Abstract: The talk aims to provide a bird view on a China program trying to develop a full suite of engineering software mainly including CAD/CAM/CAE/CAPP and PLM for those user communities who lost access to mainstream software tools resulting from recent geopolitical complexities. The speakers will share where Huawei come from, how they develop a pragmatic strategy for business continuity in parallel with advancing next generation software based on cloud, and how they will commercialize their home-grown software via Huawei Industrial Software Cloud. The Russia-China partnership is essential to accelerate implementation of the ambitious but meaningful plan. Some major engineering problems and challenges encountered during the development will also be shared for potential collaborators’ reference.

Automatic detection of manufacturing issues in CAD parts for DFM analysis

Sergey Slyadnev, Andrey Voevodin
Quaoar Studio

Abstract: This paper discusses some computational principles behind automatic manufacturability tests for CAD models of machined parts. The presented approach is a combination of automatic feature recognition supplemented with ray casting for accessibility, thickness and clearance checks. Most of the discussed approaches are applicable for different production methods, such as milling and turning (lathing) as they are purely geometric in nature. We distinguish between meshless and mesh-based methods for the analysis of manufacturing issues in a CAD part. For the mesh-based methods, two types of surface triangulation are employed: a sparse non-uniform triangulation having a relatively small number of triangles representing the geometric boundary of a part, and a dense grid covering the input part with uniform triangulation. The latter kind of mesh is constructed using quadtree-based subdivision of the UV spaces of the corresponding curvilinear trimmed surfaces.

Self-intersection computation and meshing of parametric surfaces

Xiaohong Jia
Academy of Mathematics and Systems Science, CAS

Abstract: Self-intersections of parametric surfaces are crucial to the topology determination, intersection, mesh generation, rendering of surfaces. We present an efficient and robust algorithm for computing all self-intersections of rational parametric surfaces using the technique of moving planes, which address a novel approach to the open problem on computing singularities of rational surfaces raised by Laurent Buse, Ron Goldman and Hal Schenck in 2016. Based on this algorithm, we then develop a novel approach to the accurate generation of meshes for parametric surfaces with self-intersections. The result meshes naturally adapt to self-intersection curves and therefore are easy for the follow-up geometry processing.

Rectangle-dominated conforming mesh generation algorithm for three-dimensional integrated circuits

Xin Yang, Julin Shan
Xidian University

Abstract: By stacking multiple device layers, design problems such as global interconnect scaling and bandwidth limitations of Three Dimensional Integrated Circuits (3D ICs) can be overcome. However, it is rather difficult to generate automatically a high-quality and conformal mesh for multiple 3D ICs. In this paper, a mesh generation process of conformal rectangle geometry for 3D ICs is proposed. First, a simple method is developed to decompose a multi-connected two-dimensional domain into several four-sided subregions and a structured quadrilateral mesh is generated for the rectangular subregions. A Delaunay-AFT based method is used to generate quadrilateral-dominated meshes in the non-rectangular subregions. Moreover, we propose a boundary discretization method of binary knapsack lattice to control mesh density and reflect the skin effect of conductors. We also put forward a mesh imprinting algorithm to generate a conformal mesh between multilayers. The effectiveness and reliability of the proposed method has been verified with several examples.

Possibilities of mesh generation in LOGOS software package for solving aero-hydrodynamics problems

Olga N. Borisenko, K.A. Blazhnova, A.G. Giniyatullina, E.O. Evstifeeva, M.V. Kuzmenko, V.V. Lazarev, D.M. Pankratov, N.V. Popova, D.N. Smolkina, T.E. Timaeva, T.V. Tsalko, M.V. Cherenkova, N.V. Chukhmanov, A.I. Shavkhitdinova
Russian Federal Nuclear Center — All-Russian Research Institute of Experimental Physics

Abstract: Generation of a high-quality computation mesh for numerical analysis is one of the most labor- and timeconsuming stages in preparation of a numerical model, as the success of further computations directly depends on the quality of the prepared computation mesh.

Special meshes with a non-uniform structure are necessary to simulate aero-hydrodynamics problems. They comprise two types of cells: the cells of a boundary layer (the layer of cells with the shape of polyhedral prisms on the surface of the overflown body close to the object being simulated, where the viscosity effect appears characterized by a strong gradient of the flow velocity); and the cells that fill the rest of the simulated domain (that may have the shape of a cube, a tetrahedron or, in a general case, an arbitrary polyhedron). Such structure of the mesh allows simplification of the simulation of the liquid/gas flow by dividing the flow into two domains: a thin boundary layer and a non-viscous (or frictionless) flow.

This paper provides an overview of the possibilities of mesh generation that are used to solve aerohydrodynamics problems in LOGOS software package [1]. Automatic generators of surface triangular [2] and volumetric grids are used for the preparation of computational grids when solving problems of aerohydrodynamics: by the method of clipping [3], tetrahedral [4] and polyhedral meshes [5], based on tetrahedra.

You have to set a minimum number of characteristics to generate meshes with the required parameters; mesh generation is carried out in an unattended mode. The process of preparing the computational mesh consists of constructing a triangular surface grid and a volumetric mesh based on it.

Generation of surface meshes can be carried out on the basic of models in analytical or faceted representation. This paper provides a brief description of two generators of surface meshes that are used for different representations of geometric models and describes the stages of volume mesh generation; it also presents some examples of mesh generation for the problems of aero-hydrodynamics.

References:

  1. Kozelkov A.S., Lashkin S.V., Kurkin A.A., Kornev A.V., Vialykh A.M. Parallel realization of SIMPLE method on the basis of multigrid method. Sib. J. Comput. Mat. 2020, V. 23, No 1. P. 1–22.
  2. Borisenko O.N., Lukichev A.N., Evstifeeva A.O., Pankratov D.M., Tsalko T.V., Giniyatullina A.G. Algorithms of preprocessing singularities in geometric models to generate surface triangular grids in the «logos» software package preprocessor. VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 3. P. 40–52.
  3. Smolkina D.N., Borisenko O.N., Cherenkova M.V., Giniyatullina A.G., Kuz‘menko M.V., Chukhmanov N.V., Potekhina E.V., Popova N.V., Turusov M.R. An automatic generator of unstructured polyhedral grids in the «logos» software preprocessor. VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 2. P. 25–39.
  4. Popova N.V., Borisenko O.N., Korneeva I.I., Chukhmanov N.V., Potekhina E.V., Lazarev V.V., Giniyatullina A.G. Automatic generator of unstructured tetrahedral grids with prismatic layers in the logos software package preprocessor. VANT. Ser.: Mat. Mod. Fiz. Proc. 2020. No 1. P. 43–57.
  5. Popova N.V. Automatic generator of unstructured polyhedral meshes on the base of tetrahedral meshes with prismatic layers. VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 70–83.

Development and application of advanced gridding technologies in solving complex physical problems

Wentao Zhou
Shenzhen Tenfong Technology Co. Ltd.

Abstract: Product research and development require the use of CAE (computer-aided engineering) software. Sustainable innovation under new use cases brought by the new economy calls for the development of next-generation CAE software. In this presentation, the author will show the development progress of such software with a focus on the application of advanced gridding technologies in solving complex physical problems.

The first example is overset-grid in CFD. The overset or Chimera grid approach is the construction of a grid system made up of blocks of overlapping structured or unstructured grids. Boundary information is exchanged between these grids via interpolation of the flow variables. Examples from the marine industry and the aeronautic industry (subsonic and supersonic) will be given to show the advantages of such grid system.

The second example is Cartesian grid with mesh refinement for Lattice Boltzmann method (LBM). The gridding technology will be explained and examples given to show its easiness in mesh generation and capability in capturing complex geometries without much user difficulty. Key algorithmic development is required in LBM to handle such grid for flow with high Reynolds number. Examples from the automobile industry will be presented to validate the method and show the advantages of such grid system in solving automobile aerodynamics problems.

Parallel moving adaptive mesh generation around rotating blades with guaranteed nondegeneracy of 4d space-time cells

Vladimir Garanzha, Liudmila Kudryavtseva
Dorodnicyn Computing Center FRC CSC RAS

Abstract: We present an algorithm which allows to build a moving deforming mesh with a fixed connectivity following target mesh compression zones defined by the time-dependent metric field. We construct a metric around the moving body by specifying normal and tangent target stretches which take into account the prescribed normal stretching law, principal curvatures and principal directions of the boundary, as well as the body feature size via a medial axis transform. Minimization of the barrier quasi-isometric functional is used to predict the minimization directions which serve as approximate tangents of the space-time mesh trajectories. It is guaranteed that 4d space-time cells are nondegenerate and the angle between the “time direction” and the “space plane” is bounded from below, thus, bounding the discrete velocity of the cells.

A very efficient parallel iterative linear solver based on the Kaporin second order incomplete Cholesky factorization is used along with a special time-stepping procedure, thus, allowing no more than 1–2 linear solves of the Newton-like minimization algorithm per artificial time step. It is important that the mesh deformation time step is larger compared to the viscous flow simulator time step allowing for simple mesh interpolation over time and, thus, making the total contribution of the robust but relatively expensive mesh deformer to the total wall clock time to be below 50%.

The Noisette aeroacoustic flow solver by the Prof.~Kozubskaya group (Institute of Applied Mathematics RAS) was used as a flow solver. It is based on the immersed boundary conditions (IBC) concept and mesh adaptation near the moving boundaries sharply improves the IBC accuracy. The mesh adaptation algorithm allows large Courant number computations for the flow solver. Parallel efficient of the mesh adaptation phase is comparable to that of the flow solver. We demonstrate the deforming mesh which follows realistic rotating blades of the quadrocopter inside a thin cylinder with a fixed boundary demonstrating technology which potentially can be incorporated into large-scale simulations of the various aircrafts. Evidently, the IBC concept has inherent limitations. The ways to overcome these limitations are briefly discussed.

Mesh morphing and remeshing scheme for moving boundary problem in multiphysics simulation

Qun Zhang
INTESIM Technology Co. Ltd.

Abstract: Moving boundary problem is one of the most challenging problems in multiphysics analysis. For fluid, thermal, electromagnetic, and acoustic analysis which based on unstructured grid discretization, the quality of the grid is directly related to the accuracy and the reliability of the simulation. This paper introduces the mesh morphing and remeshing technologies implemented in a commercial CAE software INTESIM, involving the application of fluid-structure interaction and electromagnetic-structure coupling analysis. This paper will cover mesh morphing scheme based on spring and elastic body solution, the grid local deformation stiffness control technology, the sliding grid technology for translational and rotational machinery, the grid layering technology, and the local remeshing technology for extreme moving boundary problems. Finally, the effectiveness of the moving boundary technology is demonstrated through multi-field coupling application cases in aerospace, rail transit, electronics, and automotive fields.

Discontinuous spectral element method for structural analysis of assemblies with geometrical issues at non-conformal curvilinear meshes

Anatoly Vershinin, Vladimir Levin, Dmitry Konovalov, Alexey Kukushkin
Lomonosov Moscow State University

Abstract: An approach to numerical solving problems of mechanics of a deformable solid on nonconformal unstructured curvilinear meshes using the discontinuous spectral element method is considered [2, 5, 11]. The computational domain is divided into subdomains, within which it is possible to discretize with conformal spectral-elemental meshes [7, 8]. On the boundaries of the subdomains, boundary conditions of the first and second kind are set, which ensure the continuity of the solution (stress-strain state) in the entire domain, including internal boundaries. An example of this problem is the structural analysis of assemblies consisting of several parts (deformable solids) in a bonded contact state. Solids interact with each other while deforming without slipping and separation along the internal boundaries (i.e. the bodies are glued to each other). The standard approach to solving such problems is imprinting the boundaries of bodies on neighboring bodies with their subsequent merging through common boundary zones. However, this approach requires conformal discretization of the entire assembly in numerical simulation, including conformal meshes on common boundaries, which often creates significant problems for industrial CAD models consisting of a large number of parts of various sizes. For example, with conformal discretization of assemblies, it is not possible to make a sharp transition from a coarse mesh to a refined one, connect meshes with different types of elements (tetrahedra, hexahedra), and build an unstructured hexahedral mesh in the entire model. Moreover, constructing a single conformal mesh in an assembly is difficult or impossible if there are geometric issues (gaps, overlaps, etc. between bodies) in the original geometric model (which often happens when importing CAD models into CAE systems), as well as in where the solids are not perfectly adjacent to each other. As a result, it is necessary to correct/modify the original CAD model (which is time consuming and not an automated process in general) to generate a mesh of an acceptable quality for the further simulation.

The presentation outlines an approach to solving the described problems related to the mesh generation for assemblies with geometrical issues which does not require that the mesh must be conformal at the boundaries between solids and construct instead of it an independent discretization in each body with their further bondind along the boundaries to ensure a continuous solution of the boundary value problem (stress-strain states) throughout the assembly. The presentation considers an algorithm for the discontinuous spectral element method based on the contact interaction of deformable solids [9, 13]. The coupled contact between the boundary elements inside the contact area is provided by direct introduction of the continuity conditions of displacements into the stiffness matrix (and into the mass matrix in the case of non-stationary problems) obtained as a result of discretization of the boundary value problem of mechanics of deformable solid on nonconformal spectral-element meshes (in this case, discretization of individual solids inside the assembly is performed conformally). This approach is a direct generalization of the classical technique for taking into account the Dirichlet conditions on displacements in the finite element method [1, 4, 6, 10]. The continuity of normal stresses in the contact areas is ensured by the corresponding additional terms in the stiffness matrix obtained from the boundary integrals over the contact zones in the framework of the weak formulation of the boundary value problem by the Galerkin method (continuity of normal stresses in a weak sense) [11, 12]. Discretization in space with a high order is provided using spectral element method on curvilinear meshes [3, 7, 8]. The described algorithm makes it possible to obtain a correct numerical solution on unstructured nonconformal meshes consisting of curvilinear spectral elements, with the possibility of setting different orders of spatial approximation in subdomains, as well as to ensure the continuity of the solution in the C-norm for the main variables of the problem (displacements) and the continuity in the L2-norm for normal stresses in contact zones (boundaries of subdomains).

Model examples are presented to verify the algorithm implemented in CAE Fidesys [14] for the numerical solution of engineering structural analysis problems on curvilinear nonconformal meshes by comparing the results of computer simulation with analytical solutions and solutions of similar problems for the case of conformal discretization: static, dynamic and modal analysis of assemblies consisting of solids with curvilinear boundaries. The robustness of the implemented software and the continuity of the obtained solution in the case of gaps/overlaps between the contacting solids are analyzed. It is shown that small gaps and overlaps in the assembly of CAD model do not affect the correctness of the obtained numerical results, and these geometric issues are automatically processed in the CAE Fidesys software using the described algorithm.

Examples of solving industrial problems of structural analysis of different CAD-models are considered.

This work is supported by the grant of the President of the Russian Federation for young scientists - doctors of science (project MD-208.2021.1.1) in the part related to a numerical solution, and by the Mathematical Center for Fundamental and Applied Mathematics (project 075-15-2019-1621) in the part related to the problem statement.

References:

  1. Abel J and Shephard M 1979 An algorithm for multipoint constraints in finite element analysis Int. J. Numer. Meth. Engng 14 pp 464–467
  2. Arnold, D., Brezzi, F., Cockburn, B., Marini D. (2002). Unified analysis of discontinuous Galerkin methods for elliptic problems: SIAM J. Numer. Anal. 39. 1749–1779.
  3. Bernardi C. and MadayY. Polynomial interpolation results in Sobolev spaces. Journal of Computational and Applied Mathematics Volume 43, Issues 1–2, 25 November 1992, ages 53-80
  4. Chow, E., Manteuffel, T., Tong, C., Wallin, B. (2001). Algebraic elimination of slide surface constraints in implicit structural analysis: Int. J. Numer. Meth. Engng 01. 1-21.
  5. Cockburn, B., Karniadakis, G., Shu Chi-Wang (2000). Discontinuous Galerkin Methods: Theory, Computation and Applications: Berlin, Springer-Verlag.
  6. Felippa C 2004 Introduction to finite element methods. Chapter 8 Multifreedom constraints I. Colorado, Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado Boulder pp 1-17
  7. Karpenko V.S., Vershinin A.V., Levin V.A., Zingerman K.M. Some results of mesh convergence estimation for the spectral element method of different orders in Fidesys industrial package // IOP Conference Series: Materials Science and Engineering. 2016. V. 158. Paper No. 012049.
  8. Konovalov D., Vershinin A., Zingerman K., Levin V. The implementation of spectral element method in a CAE system for the solution of elasticity problems on hybrid curvilinear meshes // Modelling and Simulation in Engineering. 2017. V. 2017. Article ID 1797561. P. 1–7.
  9. Kukushkin A, Konovalov D, Vershinin A and Levin V Numerical simulation in CAE Fidesys of bonded contact problems on non-conformal meshes 2019 J. Phys.: Conf. Ser. 1158 032022
  10. Shephard, M. (1984). Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process: Int. J. Numer. Meth. Engng 20. 2107-2112.
  11. A V Vershinin et al Application of variable order spectral element method on non-conformal unstructured meshes for an engineering analysis of assemblies with geometric inaccuracies 2020 IOP Conf. Ser.: Mater. Sci. Eng. 747 012033
  12. Wang, X., Prakash, A., Chen, J., Taciroglu, E. (2017) Variationally consistent coupling of non-matching discretizations for large deformation problems: Comput Mech 60. 465. DOI:10.1007/s00466-017-1417-0.
  13. Zienkiewicz O and Taylor R 2014 The Finite Element Method for Solid and Structural Mechanics Seventh Edition (Amsterdam: Elsevier)
  14. www.cae-fidesys.com

CPU/GPU parallelization of solution of convection-dominated problems for incompressible Navier-Stokes equations using the PFEM-2 method

Andrey Popov, Ilia Marchevsky
Bauman Moscow State Technical University

Abstract: Possibilities for parallelization of different operations of the Particle Finite Element Method, 2nd generation, (PFEM-2) are investigated. CPU/GPU parallelization is implemented within the framework based on the open-source deal.II C++ library. Main operations of the algorithm include the FEM step, particle transport and projection of velocity field from mesh nodes onto particles and vice versa. FEM step is parallelized over MPI using built-in functionality of deal.II as well as auxiliary libraries including p4est for domain decomposition and Trilinos for linear algebra. Due to the independency of transport of the particles along the velocity field streamlines in PFEM-2 this operation can be effectively performed using both MPI and Cuda technologies. The same applies to the projection procedures. A solver including all these techniques was tested on test problems for a two-dimensional flow past a cylindrical body on a multi-core system and a cluster with Nvidia Titan-V GPUs. Efficiency of parallel implementation for different operations of the algorithms and different technologies is shown.

Dynamic adaptive moving mesh finite volume method for Navier-Stokes equations

Alexander A. Danilov, Kirill M. Terekhov, Yuri V. Vassilevski
Marchuk Institute of Numerical Mathematics

Abstract: This work is concerned with parallel dynamic adaptive moving meshes with the solution of 4D Navier-Stokes equations. The method is applied to the blood flow problem in the moving domain of the left ventrical, reconstructed from the CT-scan. The moving mesh of the left ventrical is dynamically adapted in the areas of high vorticity to improve capturing of the flow features. For the flow approximation we use fully implicit collocated finite volume method. The methods are implemented using functionality of the INMOST platform.

Semi-analytic technique for integration of Newtonian potential and its gradient over triangular surface grid cells

Ilia Marchevsky, Sofiya Serafimova, Aliya Gumirova
Bauman Moscow State Technical University

Abstract: The integrals are considered that arise when solving boundary integral equations, which kernels is Newtonian potential or its gradient, in the case when the solution is considered to be piecewise-constant over panels, which are flat triangles. Integrals over one panel are considered which are calculated in the framework of collocations method, and the calculation technique is developed for repeated integrals over two panels arising in the Galerkin method. Exact analytical expressions suitable for practical usage are presented for single integrals over one panel; for repeated integrals a hybrid numerical-analytical scheme is proposed, which involves the extraction of singularities in the integrands and their analytical integration, as well as the numerical integration of smooth functions.

Triangular Mesh Distribution for Earthwork Calculations in Different Terrains

Hanbing Zhang, Xuhui Wang, Guoqiao You, Meng Wu
Nanjing University of Science and Technology

Abstract: In this paper, the statistical trend of the triangular mesh distribution in high-precision earthwork calculations is explored. To avoid the low efficiency of directly using an optimization algorithm in large-scale earthwork calculations, the distribution of the triangular mesh in large-scale high-precision earthwork calculations is considered by starting from the optimization of a small-scale terrain feature surface function. The specific contents of the paper are as follows. First, the optimization model for earthwork calculations is established.Second, the triangular meshes associated with different small-scale terrain features are optimized with the SLSQP algorithm, and the optimized triangular meshes corresponding to the high-precision earthwork calculations for 30 examples are obtained. Third, through a correlation analysis of the optimized triangular meshes, the distribution of the optimized triangular mesh is studied, and the results provide a theoretical basis for the development of a direct generation algorithm for triangular mesh to avoid using an optimization algorithm in large-scale high-precision earthwork calculations.

Using neural network to solve inverse problem of seismological exploration in fractured medium

Maksim V. Muratov, Denis S. Konov, Dmitrij I. Petrov, Igor B. Petrov
Moscow Institute of Physics and Technology

Abstract: Inverse problen of seismological explorations are very important for searching and development of natural resources. More sophisticated analysis of probable deposits requires modern computational models. The work is devoted to an effort of using convolutional neural networks to reconstruct geological medium inner structure, particularly its fractured parts position and other parameters. Several cracks configurations were regarded. Data for training and testing of the network was computed using linear elasticity model and grid-characteristics method.

Parallel Algorithm for Incompressible Flow Simulation Based on the LS-STAG and Domain Decomposition Methods

Viktoria D. Karabanova, Ilia K. Marchevsky, Valeria V. Puzikova
Ivannikov Institute for System Programming RAS

Abstract: The problem of incompressible flow simulation around rigid bodies of arbitrary shape is considered. The LS-STAG immersed boundary method is used for its numerical solving. This method is based on the accurate discretization of the governing equations in cells that are cut by the boundary and provides the second order of accuracy. The aim of the research is to develop parallel algorithm for incompressible flow simulation based on the LS-STAG and the Schur complement methods to accelerate one of the most timeconsuming parts of the LS-STAG algorithm—solving of the Poisson equation for the pressure function. The developed algorithm is implemented as an object-oriented code on C++ using MPI technology for parallelization. The problem of two-dimensional flow simulation around a fixed circular airfoil was solved to estimate the efficiency of the obtained implementation. Currently, we are still performing calculations on more cores on tasks with a more detailed grid.