Russian  version

	Working group   "Numerical geometry, grid generation  and high performance computing   A.A. Dorodnicyn Computing Center  Federal research Center  of Computer Science and Control Russian Academy of Sciences, Moscow

Contents:

Working group:

• Garanzha Vladimir Anatolyevich Dr. Sci., professor RAS, head of group;
  
• Kaporin Igor Evgenievich Dr.Sci. principal researcher;
  
• Kudryavtseva Liudmila Nikolaevna, PhD (Cand. Sci)  researcher;
  
• Belokrys-Fedotov Alexey Igorevich,  researcher.

Research directions:

• Numerical geometry problems: surface reconstruction and parameterization, integration of grid generation with CAD/CAE, geometric modeling and optimization, mappings, deformations and morphings, geometric methods in molecular biology,computational anatomy;
• Computation grid generation methods: 2D, surface and 3D grids, local and global mesh quality criteria, structured and unstructured grids, Voronoi-Delaunay methods, geometric quality measures and numerical errors, symmetry and invariance in grid generation, barrier variational methods, adaptive moving grids, mesh stability and sensitivity analysis, mesh untangling.
• Numerical modeling and mesh adaptation, efficient iterative solutions of variational problems, mesh-based and "meshless" methods, domain decomposition, graph partitioning and parallel computing;
• Theoretical foundations of numerical geometry and grid generation: harmonic, conformal and quasi-isometric mappings, mappings of bounded distortion, foundations of elasticity and crystallography with large deformations, discrete curvatures and manifolds of bounded curvature,  approximations by polyhedral manifolds.
• Education and knowledge structuring in numerical geometry and grid generation.
• Problems related to square matrices: development, analysis, and implementation of standard solvers for large-scale algebraic problems using supercomputers. In particular, parallel iterative linear solvers are under development. The research is mainly concentrated at parallel preconditionings (approximate matrix inversion) based on reduction to special optimization problems.
  
• Development of robust algorithms for undirected graph partitioning with account of balancing, edge cut, component connectivity, and special restrictions (such as integrity of prespecified connected subgraphs).  The problem is of primary importance for the efficient organization of parallel computations with sparse matrices (including the construction of preconditionings) as well as for the problem of large-scale computational grid construction and optimization.
  
• Problems, related to rectangular matrices such as normalized tight frames: the development of optimality criterions similar to the equiangularity condition and search for deterministic theoretical bounds and practical constructions for tight frames with good restricted isometry properties.  Tight frames are a natural generalization of orthogonal matrices and have numerous applications in many modern algorithms of digital data processing (retrieval, coding, compression, etc.)   Despite of intense worldwide research during last decades, there are still many important open problems in the area connected with the theory of optimal frames.
  

Projects:

• smesher project: generator of monoblock structured and aggregated block-structured meshes around bodies with wings and tails;


• prismatic_qi3d_poly project: automatic generator of thick prismatic layers around complicated bodies;
  


• sotm project: generator of Delaunay and polyhedral meshes for analitically defined bodies;

• qimove project: parallel moving deforming mesh generator;

• radical-Delaunay polygonal and polyhedral Delaunay and Voronoi meshing;
  

• ord_adj  project:  decomposition of undirected graphs with constraints;

•  vc_ran_slau  project: massively parallel solver for sparse linear systems; 
  

• vc_ran_eigv project: massively parallel solver for partial spectral problem for sparse SPD matrices.
  
  

Thematic conferences: 

International conference "Numerical geometry, grid generation and scientific computing " Moscow, November, 2020.  Conference homepage: http://www.ccas.ru/gridgen/numgrid2020

International conference "Numerical geometry, grid generation and scientific computing " Moscow, December 3-5, 2018.  Conference homepage: http://www.ccas.ru/gridgen/numgrid2018

International conference "Numerical geometry, grid generation and scientific computing " Moscow, October 31 - November 2, 2016.  Conference homepage: http://www.ccas.ru/gridgen/numgrid2016