INMOST

"The INMOST mathematical modeling toolkit helps a user to formulate and solve a problem of partial differential equations on general meshes in parallel. The current work covers: data structure description for efficient distributed unstructured mesh representation, interrelation of mesh elements with maximal flexibility of supported types of the mesh, treatment of ghost cells and distribution of mesh data for parallel execution, flexible templates for the implementation of numerical schemes, convenient framework for parallel linear systems assembly and solution. We also present aspects of the implementation and a simple example of application of INMOST to the solution of anisotropic diffusion problem. On this example we demonstrate the application of INMOST for all the stages of numerical modeling: construction of the distributed mesh, assignment of the problem data to the elements, problem discretization on local domain, solution of linear system in parallel. INMOST is a newly developed, flexible and efficient numerical analysis framework that provides scientists the infrastructure for designing highly scalable high performance applications for mathematical modeling.

Links below contain detailed technical description of the implementation of particular data structures and algorithms. For general use see User Guides.

• Domain for operations on geometrical model of the domain. (not implemented)
• Mesh for operations with the discrete representation of the domain.
• Manipulations with mesh Elements.
• Representation of Sets of elements.
• Mesh Data organization and access.
• Mesh Modification algorithms.
• Distributed Parallel algorithms.
• Distributed Parallel Modification of the mesh.
• File Formats for the mesh.
• Partitioner for separation of the mesh into parts.
• Internal Partitioners.
• External Partitioners.
• Solver for solution of the sparse system of linear equations.
• Vector for representation of the solution and the right hand side in dense vector.
• Row for representation of the sparse vector used for Matrix.
• Row Merger for addition of multiple sparse vectors.
• Matrix for representation of the Jacobian matrix of first derivatives.
• Hessian Row for the representation of the sparse matrix of second derivatives.
• Hessian Row Merger for the addition of multiple sparse matrices of second derivatives.
• Hessian Matrix for representation of the Hessian tensor of second derivatives.
• Internal Solvers for the solution of the sparse system.
• External Solvers for the solution of the sparse system.
• Linear algebra on Dense Matrices.
• Algorithms on dense matrices.
• Representation of a dense matrix and sub-matrix.
• Interoperation with mesh data.
• Interoperation with automatic differentiation.
• Methods for Automatic differentiation.
• Expressions for algebra of variables with derivatives.
• Automatizator for interoperation with mesh.
• Variable Expressions for construction of operations to be performed on mesh elements using expressions.
• Residual for the automated assembly of the Jacobian matrix, Hessian tensor and right hand side for the system of nonlinear equations.
• Working with Dense Matrices of variables with derivatives.
• Nonlinear solver (not implemented)
• Optimization (not implemented)
• Supplementary data structures and algorithms.

References

• K. Terekhov. Application of octree-type adaptive grids to solution of filtration and hydrodynamics problems. Ph.D. Thesis, INM RAS, Moscow, 2013 (in Russian) (PDF)
  
• Yu. Vassilevski, I. Konshin, G. Kopytov, K. Terekhov. INMOST – a software platform and a graphical environment for development of parallel numerical models on general meshes. ISBN 978-5-211-06480-5. Lomonosov Moscow State Univ. Publ., Moscow, 2013, 144 p. (in Russian) (PDF)
  
• A. A. Danilov, K. M. Terekhov, I. N. Konshin, Y. V. Vassilevski. Parallel software platform INMOST: a framework for numerical modeling, Supercomputing Frontiers and Innovations (2015) V.2, No.4, 55-66. (PDF)
  
• A. Danilov, K. Terekhov, I. Konshin, Yu. Vassilevski, The structure of INMOST program platform and its usage for numerical modeling problems, In: Proc. of Russian Supercomputing Days 2015, Moscow State Univ. Publ., Moscow, 2015, pp. 104-109. (PDF)
  
• Yu. Vassilevski, I. Konshin, G. Kopytov, K. Terekhov, Software platform and graphical environment for development of parallel numerical models on general meshes. In: Proc. of Int. Conf. "Numerical geometry, grid generation and scientific computing" (NUMGRID2012) December 17-19, 2012. Dorodnicyn Computing Center of Russian Academy of Sciences, Moscow, 2012. (in Russian) (slides)
  
• D. V. Bagaev, A. I. Burachkovski, I. N. Konshin, K. D. Terekhov, INMOST software platform (development in 2016): Dynamic distributed grids, automatic differentiation and linear solvers, In: Proc. of the Third meeting of national developers of CFD codes "National CFD codes - 2016", December 3-4, 2016, IMM RAS, Moscow. (in Russian) (slides)
  
• D. V. Bagaev, A. I. Burachkovski, A. A. Danilov, I. N. Konshin, K. D. Terekhov, Development of {INMOST} software platform: dynamic grids, linear solvers and automatic differentiation, In: Russian Supercomputing Days: Proc. of the Int. Conf. (September 26-27, 2016, Moscow, Russia). Moscow State University, Moscow, 2016, pp. 543-555 (in Russian) (PDF)
  

See related publications for various applications of INMOST."

https://github.com/INMOST-DEV/INMOST