Parallel software platform INMOST: a framework for numerical modeling

Alexander A. Danilov; Kirill M. Terekhov; Igor N. Konshin; Yuri V. Vassilevski

doi:10.14529/jsfi150404

Authors

Alexander A. Danilov Institute of Numerical Mathematics RAS, Moscow
Kirill M. Terekhov Stanford University, Stanford
Igor N. Konshin Institute of Numerical Mathematics RAS, Moscow
Yuri V. Vassilevski Institute of Numerical Mathematics RAS, Moscow

DOI:

https://doi.org/10.14529/jsfi150404

Abstract

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.

References

Danilov AA, Vassilevski YV. A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes. Russian Journal of Numerical Analysis and Mathematical Modelling. 2009;24(3):207-227.

Garimella RV. MSTK - A Flexible Infrastructure Library for Developing Mesh Based Applications. In: 13th International Meshing Roundtable, September 19-22, 2004, Williamsburg, Virginia, USA, Proceedings; 2004. p. 203-212.

Edwards HC, Williams AB, Sjaardema GD, Baur DG, Cochran WK. SIERRA Toolkit Computational Mesh Conceptual Model. Technical Report SAND2010-1192, Sandia National Laboratories; 2010.

Tautges TJ. MOAB-SD: Integrated Structured and Unstructured Mesh Representation. Engineering With Computers. 2004;20(3):286-293.

Tautges TJ, Meyers R, Merkley K, Stimpson C, Ernst C. MOAB: A Mesh-Oriented Database. Technical Report SAND2004-1592, Sandia National Laboratories; 2004.

Seol ES. FMDB: flexible Distributed Mesh Database for Parallel Automated Adaptive Analysis, Ph.D. Thesis, Rensselaer Polytechnic Institute; 2005.

Balay S, Abhyankar S, Adams MF, Brown J, Brune P, Buschelman K, et al. PETSc users manual. Argonne National Laboratory, ANL-95/11 - Revision 3.5; 2014.

Balay S, Gropp WD, McInnes LC, Smith BF. Efficient Management of Parallelism in Object Oriented Numerical Software Libraries. In: Modern Software Tools in Scientific Computing, Birkhauser Press; 1997. p. 163-202.

Heroux MA, Phipps ET, Salinger AG, Thornquist HK, Tuminaro RS, Willenbring JM, et al. An overview of the Trilinos project. ACM Transactions on Mathematical Software. 2005;31(3):397-423.

Kapyrin I, Konshin I, Kopytov G, Nikitin K, Vassilevski Y. Hydrogeological modeling in radioactive waste disposal safety assessment using the GeRa code. Russian Supercomputing Days: Proceedings of the international conference (September 28-29, 2015, Moscow, Russia). Moscow State University; 2015. p. 122-132. Russian.

Terekhov KM, Nikitin KD, Olshanskii MA, Vassilevski YV. A semi-Largangian method on dynamically adapted octree meshes, to appear in Rus.J.Num.Anal.Math.Model.

Konshin I, Kaporin I, Nikitin K, Vassilevski Y. Parallel linear systems solution for multiphase flow problems in the INMOST framework. Russian Supercomputing Days: Proceedings of the international conference (September 28-29, 2015, Moscow, Russia). Moscow State University; 2015. p. 96-103.

Garimella RV. Mesh Data Structure Selection for Mesh Generation and FEA Applications. International Journal of Numerical Methods in Engineering. 2002;55(4):451-478.

Bertsekas DP, Tsitsiklis JN. Parallel and Distributed Computation: Numerical Methods. Prentice-Hall; 1989.

Boman EG, Catalyurek UV, Chevalier C, Devine KD. The Zoltan and Isorropia parallel toolkits for combinatorial scientific computing: partitioning, ordering, and coloring. Scientific Programming. 2012;20(2):129-150.

Schloegel K, Karypis G, Kumar V. Parallel static and dynamic multi-constraint graph partitioning. Concurrency and Computation: Practice and Experience. 2002;14(3):219-240.

Vassilevski Y, Konshin I, Kopytov G, Terekhov K. INMOST - a software platform and a graphical environment for development of parallel numerical models on general meshes. Moscow State Univ. Publ., Moscow; 2013. Russian.

Terekhov K. An application of the octree-type adaptive grids to the solution of filtration and hydrodynamics problems. PhD Thesis, Institute of Numerical Mathematics RAS, Moscow; 2013. Russian.