Difference between revisions of "Medusa"

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* [[Coding style | Coding style]]
 
* [[Coding style | Coding style]]
 
* [[Wiki editing guide | Wiki editing and backup guide]]
 
* [[Wiki editing guide | Wiki editing and backup guide]]
 +
 +
== 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]]
 +
* [[Relaxation of the nodal distribution]]
 +
* [[Refinement of the nodal distribution]]
 +
* [[k-d tree|''k''-d tree and other spatial search structures]]
 +
* [[Solving system | Solving linear system - including over and underdetermined systems]]
 +
* [[Weighted Least Squares (WLS)]]
 +
* [[Computation of shape functions]]
 +
* [[Radial basis function-generated finite differences (RBF-FD)]]
 +
* [[Ghost nodes (theory)]]
 +
* [[Integrators for time stepping]]
  
 
== Examples ==
 
== Examples ==
Line 28: Line 41:
 
* [[Coupled domains]]
 
* [[Coupled domains]]
 
* [[Parametric domains | Parametric domains – Curved surface with variable density]]
 
* [[Parametric domains | Parametric domains – Curved surface with variable density]]
−
* [[NURBS domains | Domains modeled with non-uniform rational basis spline's (NURBS)]]
+
* [[NURBS domains | Domains modeled with non-uniform rational basis splines (NURBS)]]
 
* [[Determining the interior of the domain by oversampling the boundary]]
 
* [[Determining the interior of the domain by oversampling the boundary]]
 
* [[Computer-aided design - Importing IGES and STEP files]]
 
* [[Computer-aided design - Importing IGES and STEP files]]
−
* [[Realistic 3D models|Working with surface mesh 3D models]]
+
* [[Realistic 3D models|Working with 3D surface mesh models ]]
 
* [[customization | Operator customization]]
 
* [[customization | Operator customization]]
 
* [[Ghost nodes]]
 
* [[Ghost nodes]]
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* [[Wave equation]]
 
* [[Wave equation]]
 
* [[Cahn-Hilliard equation]]
 
* [[Cahn-Hilliard equation]]
−
* [[Non-Newtonian_fluid_example | Non-Newtonian fluid]]
+
* [[Fluid mechanics]]
−
* [[Meshless Lattice Boltzmann method]]
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* [[Solid Mechanics | Solid mechanics]]
−
 
 
−
== 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]]
 
−
* [[Relaxation of the nodal distribution]]
 
−
* [[Refinement of the nodal distribution]]
 
−
* [[k-d tree|''k''-d tree]] and other spatial search structures
 
−
* Solving [[Solving linear systems | linear systems]], [[Solving overdetermined systems | overdetermined]] and [[Solving underdetermined systems | underdetermined]]
 
−
* [[Weighted Least Squares (WLS)]]
 
−
* [[Computation of shape functions]]
 
−
* [[Radial basis function-generated finite differences (RBF-FD)]]
 
−
* [[Ghost nodes (theory)]]
 
−
* [[Integrators for time stepping]]
 
  
 
== Discussions / Applications ==
 
== Discussions / Applications ==
Line 67: Line 67:
 
* [[Fluid Mechanics]]
 
* [[Fluid Mechanics]]
 
** [[Lid driven cavity]]
 
** [[Lid driven cavity]]
 +
** [[Burgers' equation]]
 
** [[de Vahl Davis natural convection test]]
 
** [[de Vahl Davis natural convection test]]
 
** [[Natural convection in 3D irregular domain]]
 
** [[Natural convection in 3D irregular domain]]
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** [[Heart rate variability detection]]
 
** [[Heart rate variability detection]]
 
** [[Bioheat equation]]
 
** [[Bioheat equation]]
 +
* [[Meshless FDM]]
  
 
== Performance analyses ==
 
== Performance analyses ==
Line 101: Line 103:
 
== References ==
 
== References ==
  
−
For all pre-prints check https://e6.ijs.si/ParallelAndDistributedSystems/publications/
+
For all related papers including conference contributions, monographs and book chapters check https://e6.ijs.si/ParallelAndDistributedSystems/publications/
 +
 
 +
{{Box-round|title= Selected papers |
 +
 
 +
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/153678339.pdf M. Jančič, G. Kosec; Strong form mesh‑free hp‑adaptive solution of linear elasticity problem, Engineering with computers, vol. 39, 2023 [DOI: 10.1007/s00366-023-01843-6]]
 +
 
 +
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/98533123.pdf 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]]
  
−
* [https://e6.ijs.si/ParallelAndDistributedSystems/publications/98533123.pdf 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]]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/69777155.pdf 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]]
  
−
* 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/56730115.pdf 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]]
  
−
* [https://e6.ijs.si/ParallelAndDistributedSystems/publications/56730115.pdf 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]]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/52715011.pdf 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]
  
−
* [https://e6.ijs.si/ParallelAndDistributedSystems/publications/52715011.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32782887.pdf J. Slak, G. Kosec; On generation of node distributions for meshless PDE discretizations, SIAM journal on scientific computing, vol. 41, 2019 [DOI: 10.1137/18M1231456]
  
−
* [https://e6.ijs.si/ParallelAndDistributedSystems/publications/32782887.pdf Slak J., Kosec G., On Generation of Node Distributions for Meshless PDE Discretizations, SIAM Journal on Scientific Computing, 41(5), A3202]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32424999.pdf G. Kosec, J. Slak, M. Depolli, R. Trobec, K. Pereira, S. Tomar, T. Jacquemin, S. Bordas, M. Wahab; Weak and strong from meshless methods for linear elastic problem under fretting contact conditions, Tribology international, vol. 138, 2019]
  
−
* [https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32230439.pdf J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/31107623.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/32388135.pdf M. Maksić, V. Djurica, A. Souvent, J. Slak, M. Depolli, G. Kosec; Cooling of overhead power lines due to the natural convection, International journal of electrical power & energy systems, 2019]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/29639719.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/31107623.pdf J. Slak, G. Kosec; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain, Engineering analysis with boundary elements, vol. 100, 2019]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/29512743.pdf Kosec G., A local numerical solution of a fluid-flow problem on an irregular domain. Advances in engineering software. 2016;7]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/29639719.pdf M. Depolli, G. Kosec; 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]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/27912487.pdf Kosec G., Trobec R., Simulation of semiconductor devices with a local numerical approach. Engineering analysis with boundary elements. 2015;69-75]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/29512743.pdf G. Kosec; A local numerical solution of a fluid-flow problem on an irregular domain, Advances in engineering software, vol. 120, 2018 [DOI: 10.1016/j.advengsoft.2016.05.010]]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/3218939.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/27912487.pdf G. Kosec, R. Trobec; Simulation of semiconductor devices with a local numerical approach, Engineering analysis with boundary elements, 2015 [DOI: 10.1016/j.enganabound.2014.07.013]]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/27339815.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/3218939.pdf G. Kosec, B. Šarler; Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method, Engineering analysis with boundary elements]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/26785063.pdf Kosec G., Zinterhof P., Local strong form meshless method on multiple Graphics Processing Units. Computer modeling in engineering & sciences. 2013;91:377-396;]
+
[http://comms.ijs.si/~gkosec/data/papers/27339815.pdf G. Kosec, M. Depolli, A. Rashkovska, R. Trobec; Super linear speedup in a local parallel meshless solution of thermo-fluid problem, Computers & Structures, vol. 133, 2014]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/KosecSarlerBurgers.pdf Kosec G., Šarler B., H-adaptive local radial basis function collocation meshless method. Computers, materials & continua. 2011;26:227-253]
+
[http://comms.ijs.si/~gkosec/data/papers/26785063.pdf G. Kosec, P. Zinterhof; Local strong form meshless method on multiple Graphics Processing Units, Computer modeling in engineering & sciences, vol. 91, 2013]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/EABE2499.pdf 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;]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/2599419.pdf G. Kosec, B. Šarler; Solution of a low Prandtl number natural convection benchmark by a local meshless method, International journal of numerical methods for heat & fluid flow]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/KosecZaloznikSarlerCombeauSegregation.pdf Kosec G, Zaloznik M, Sarler B, Combeau H. A Meshless Approach Towards Solution of Macrosegregation Phenomena. CMC: Computers, Materials, & Continua. 2011;580:1-27 ]
+
[http://comms.ijs.si/~gkosec/data/papers/EABE2499.pdf R. Trobec, G. Kosec, M. Šterk, B. Šarler; Comparison of local weak and strong form meshless methods for 2-D diffusion equation, Engineering analysis with boundary elements, vol. 36, 2012]
  
−
* [http://comms.ijs.si/~gkosec/data/papers/KosecSarlerNS2008.pdf 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]
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/1905659.pdf G. Kosec, M. Založnik, B. Šarler, H. Combeau; A meshless approach towards solution of macrosegregation phenomena, Computers, materials & continua : CMC, vol. 22, 2011 ]
  
−
*  Trobec R., Kosec G., Parallel Scientific Computing, ISBN: 978-3-319-17072-5 (Print) 978-3-319-17073-2.
+
[https://e6.ijs.si/ParallelAndDistributedSystems/publications/992507.pdf G. Kosec, B. Šarler; Solution of thermo-fluid problems by collocation with local pressure correction, International journal of numerical methods for heat & fluid flow, vol.18, 2008]
  
−
*  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.
+
R. Trobec, G. Kosec; Parallel scientific computing : theory, algorithms, and applications of mesh based and meshless methods, 2015
  
−
*  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.
+
}}
  
 
==Related pages==
 
==Related pages==
 
* http://e6.ijs.si/ParallelAndDistributedSystems/products/medusa/
 
* http://e6.ijs.si/ParallelAndDistributedSystems/products/medusa/

Latest revision as of 13:55, 12 March 2024

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

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.

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.

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

  • 17:11, 26 August 2024 :: Burgers'_equation
  • 14:31, 12 July 2024 :: Customization


Miscellaneous

References

For all related papers including conference contributions, monographs and book chapters check https://e6.ijs.si/ParallelAndDistributedSystems/publications/

edit 

Selected papers

M. Jančič, G. Kosec; Strong form mesh‑free hp‑adaptive solution of linear elasticity problem, Engineering with computers, vol. 39, 2023 [DOI: 10.1007/s00366-023-01843-6]

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]

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]

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]

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

J. Slak, G. Kosec; On generation of node distributions for meshless PDE discretizations, SIAM journal on scientific computing, vol. 41, 2019 [DOI: 10.1137/18M1231456

G. Kosec, J. Slak, M. Depolli, R. Trobec, K. Pereira, S. Tomar, T. Jacquemin, S. Bordas, M. Wahab; Weak and strong from meshless methods for linear elastic problem under fretting contact conditions, Tribology international, vol. 138, 2019

J. Slak, G. Kosec; Adaptive radial basis function-generated finite differences method for contact problems, International journal for numerical methods in engineering, vol. 119, 2019 [DOI: 10.1002/nme.6067]

M. Maksić, V. Djurica, A. Souvent, J. Slak, M. Depolli, G. Kosec; Cooling of overhead power lines due to the natural convection, International journal of electrical power & energy systems, 2019

J. Slak, G. Kosec; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain, Engineering analysis with boundary elements, vol. 100, 2019

M. Depolli, G. Kosec; 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

G. Kosec; A local numerical solution of a fluid-flow problem on an irregular domain, Advances in engineering software, vol. 120, 2018 [DOI: 10.1016/j.advengsoft.2016.05.010]

G. Kosec, R. Trobec; Simulation of semiconductor devices with a local numerical approach, Engineering analysis with boundary elements, 2015 [DOI: 10.1016/j.enganabound.2014.07.013]

G. Kosec, B. Šarler; Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method, Engineering analysis with boundary elements

G. Kosec, M. Depolli, A. Rashkovska, R. Trobec; Super linear speedup in a local parallel meshless solution of thermo-fluid problem, Computers & Structures, vol. 133, 2014

G. Kosec, P. Zinterhof; Local strong form meshless method on multiple Graphics Processing Units, Computer modeling in engineering & sciences, vol. 91, 2013

G. Kosec, B. Šarler; Solution of a low Prandtl number natural convection benchmark by a local meshless method, International journal of numerical methods for heat & fluid flow

R. Trobec, G. Kosec, M. Šterk, B. Šarler; Comparison of local weak and strong form meshless methods for 2-D diffusion equation, Engineering analysis with boundary elements, vol. 36, 2012

G. Kosec, M. Založnik, B. Šarler, H. Combeau; A meshless approach towards solution of macrosegregation phenomena, Computers, materials & continua : CMC, vol. 22, 2011

G. Kosec, B. Šarler; Solution of thermo-fluid problems by collocation with local pressure correction, International journal of numerical methods for heat & fluid flow, vol.18, 2008

R. Trobec, G. Kosec; Parallel scientific computing : theory, algorithms, and applications of mesh based and meshless methods, 2015


Related pages

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