Medusa

From Medusa: Coordinate Free Mehless Method implementation
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Welcome to the Medusa wiki. To visit the main website, go to http://e6.ijs.si/medusa/.

In Parallel and Distributed Systems Laboratory we are working on a C++ library that is first and foremost focused on tools for solving Partial Differential Equations by meshless methods. The basic idea is to create generic codes for tools that are needed for solving not only PDEs but many other problems, e.g. Moving Least Squares approximation, $k$-d tree, domain generation engines, etc. We call this open source meshless project Medusa: Coordinate Free Meshless Method implementation (MM).

Technical details about code and examples can be found on our documentation page and Gitlab repository. Alt text Alt text

This wiki site is meant for more relaxed discussions about general principles, possible and already implemented applications, preliminary analyses, etc. Note, that there are many grammatical mistakes, typos, stupid sentences, etc. This wiki is meant for quick information exchange and therefore we do not invest a lot of energy into styling :).

Documentation

Examples

In this section we present exact examples. Each of the below solutions can be found also in in the repository under examples. More explanation about the physical background and solution procedure can be found in following sections.

Building blocks

Medusa is modular coordinate-free parallel implementation of a numerical framework designed, but not limited to, for solving PDEs. In this section we present main modules of the library that can be also used as a standalone tools.

Discussions / Applications

This section is meant for general discussion about the physical background of the examples, the solution procedures, various applications, etc. Note, that code snippets presented in discussion might not reflect the actual state of Medusa.

Performance analyses

Last changes

  • 16:55, 23 April 2024 :: Burgers'_equation
  • 16:24, 23 March 2024 :: Hyperviscosity
  • 14:36, 13 March 2024 :: Meshless_FDM
  • 14:55, 12 March 2024 :: Medusa
  • 15:23, 2 March 2024 :: Fluid_Mechanics


Miscellaneous

References

For all pre-prints check https://e6.ijs.si/ParallelAndDistributedSystems/publications/

  1. M. Depolli, J. Slak, G. Kosec; Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs, Computers & Structures, 2022 [DOI: 10.1016/j.compstruc.2022.106773]
  2. J. Slak, G. Kosec; Medusa : A C++ library for solving PDEs using strong form mesh-free methods, ACM transactions on mathematical software, vol. 47, 2021 [DOI: 10.1145/3450966]
  3. U. Duh, G. Kosec, J. Slak; Fast variable density node generation on parametric surfaces with application to mesh-free methods, SIAM journal on scientific computing, vol. 43, 2021 [DOI: 10.1137/20M1325642]
  4. M. Jančič, J. Slak, G. Kosec; Monomial augmentation guidelines for RBF-FD from accuracy versus computational time perspective, Journal of scientific computing, vol. 87, 2021 [DOI: 10.1007/s10915-020-01401-y
  5. Slak J., Kosec G., On Generation of Node Distributions for Meshless PDE Discretizations, SIAM Journal on Scientific Computing, 41(5), A3202
  6. Slak J., Kosec G. Adaptive radial basis function-generated finite differences method for contact problems. International journal for numerical methods in engineering, ISSN 0029-5981
  7. Slak J., Kosec G.; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain. Engineering analysis with boundary elements. 2018;11
  8. Depolli, M., Kosec, G., Assessment of differential evolution for multi-objective optimization in a natural convection problem solved by a local meshless method. Engineering optimization, 2017, vol. 49, no. 4, pp. 675-692
  9. Kosec G., A local numerical solution of a fluid-flow problem on an irregular domain. Advances in engineering software. 2016;7
  10. Kosec G., Trobec R., Simulation of semiconductor devices with a local numerical approach. Engineering analysis with boundary elements. 2015;69-75
  11. Kosec G., Šarler B., Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method. Engineering analysis with boundary elements. 2014;36-44
  12. Kosec G., Depolli M., Rashkovska A., Trobec R., Super linear speedup in a local parallel meshless solution of thermo-fluid problem. Computers & Structures. 2014;133:30-38
  13. Kosec G., Zinterhof P., Local strong form meshless method on multiple Graphics Processing Units. Computer modeling in engineering & sciences. 2013;91:377-396;
  14. Trobec R., Kosec G., Šterk M., Šarler B., Comparison of local weak and strong form meshless methods for 2-D diffusion equation. Engineering analysis with boundary elements. 2012;36:310-321;
  15. Kosec G, Zaloznik M, Sarler B, Combeau H. A Meshless Approach Towards Solution of Macrosegregation Phenomena. CMC: Computers, Materials, & Continua. 2011;580:1-27
  16. Kosec G, Sarler B. Solution of thermo-fluid problems by collocation with local pressure correction. International Journal of Numerical Methods for Heat & Fluid Flow. 2008;18:868-82
  17. Trobec R., Kosec G., Parallel Scientific Computing, ISBN: 978-3-319-17072-5 (Print) 978-3-319-17073-2.

Related pages

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