Medusa
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, examples, and can be found on our documentation page and the code. 
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 :).
Contents
Documentation
- Code on Gitlab
- Installation and building
- Including this library in your project
- Running tests
- Technical documentation
- Coding style
- Wiki editing and backup guide
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.
- Philosophy of examples and how to run them
- Poisson's equation
- Heat equation
- Linear elasticity
- Complex-valued problems
- Coupled domains
- Parametric domains – Curved surface with variable density
- Customization example: Biharmonic equation
- Ghost nodes
- Electromagnetic scattering
- Schrödinger equation
- Wave equation
- Meshless Lattice Boltzmann method
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.
- Positioning of computational nodes
- k-d tree and other spatial search structures
- Solving linear systems, overdetermined and underdetermined
- Moving Least Squares (MLS)
- Meshless Local Strong Form Method (MLSM)
- Radial basis function-generated finite differences (RBF-FD)
- Ghost nodes (theory)
- Computation of shape functions
- Integrators for time stepping
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.
- Basic PDE solutions
- Adaptivity
- Solid Mechanics
- Fluid Mechanics
- Other applications
Performance analyses
- Execution on Intel® Xeon Phi™ co-processor
- 1D MLSM and FDM comparison
- Execution overheads due to clumsy types::technical report
- Solving sparse systems
- Eigen paralelization
Last changes
- 17:11, 26 August 2024 :: Burgers'_equation
- 14:31, 12 July 2024 :: Customization
Miscellaneous
- FAQ - Frequently asked questions.
- List of wiki contributors
- List of library contributors: See the official website
References
- 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 manuscript
- 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 ; manuscript
- 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 ;manuscript
- Kosec G., A local numerical solution of a fluid-flow problem on an irregular domain. Advances in engineering software. 2016;7 ; [29512743] ; manuscript
- Kosec G., Trobec R., Simulation of semiconductor devices with a local numerical approach. Engineering analysis with boundary elements. 2015;69-75; [27912487] ; manuscript
- 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; manuscript
- 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; manuscript
- Kosec G., Zinterhof P., Local strong form meshless method on multiple Graphics Processing Units. Computer modeling in engineering & sciences. 2013;91:377-396; manuscript
- Kosec G., Šarler B., H-adaptive local radial basis function collocation meshless method. Computers, materials & continua. 2011;26:227-253; manuscript
- 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; manuscript
- Kosec G, Zaloznik M, Sarler B, Combeau H. A Meshless Approach Towards Solution of Macrosegregation Phenomena. CMC: Computers, Materials, & Continua. 2011;580:1-27 manuscript
- 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 manuscript
- Trobec R., Kosec G., Parallel Scientific Computing, ISBN: 978-3-319-17072-5 (Print) 978-3-319-17073-2.
- Slak, J., Kosec, G.. Detection of heart rate variability from a wearable differential ECG device., MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938, pp 450-455.
- Kolman, M., Kosec, G. Correlation between attenuation of 20 GHz satellite communication link and liquid water content in the atmosphere. MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938. pp. 308-313.
