Medusa
From Medusa: Coordinate Free Mehless Method implementation
Library for solving PDEs
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, kD-tree, domain generation engines, etc.
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.
Contents
Building blocks
- Moving Least Squares (MLS)
- Kd Tree
- Positioning of computational nodes
- Meshless Local Strong Form Method (MLSM)
Applications
- Basic MLSM solutions
- Attenuation of satellite communication
- Heart rate variability detection
- Dynamic Thermal Rating of over head lines
- Solid Mechanics
Performance analyses
- Execution on Intel® Xeon Phi™ co-processor
- 1D MLSM and FDM comparison
- Execution overheads due to clumsy types::technical report
Documentation
- Code and README on Gitlab
- Installation and building
- Running unit tests
- Technical documentation
- Coding style
- Wiki editing and backup guide
FAQ
Also see Frequently asked questions.
References
- 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.
- Trobec R., Šterk M., Robič B., Computational complexity and parallelization of the meshless local Petrov-Galerkin methods. Computers & Structures. 2009;87:81-90; [21895463]
- Šterk M., Trobec R., Meshless solution of a diffusion equation with parameter optimization and error analysis. Engineering analysis with boundary elements. 2008;32:567-577; [21305383]
