Medusa

Library for solving PDEse

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 http://www-e6.ijs.si/ParallelAndDistributedSystems/MeshlessMachine/technical_docs/html/ and the code https://gitlab.com/e62Lab/e62numcodes

This wiki site is meant for more relaxed discussions about ideas, applications, preliminary analyses, etc.

Background

• Moving least squares (MLS)
• Meshless Local Strong Form Method (MLSM)

Applications

• Solving Diffusion Equation
• Attenuation of satellite communication
• Heart rate variability detection
• Solid Mechanics

Preliminary analyses

• Execution on Intel® Xeon Phi™ co processor
• Execution overheads due to clumsy types

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; [3218939] :: 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; [27339815] :: manuscript
• Kosec G., Zinterhof P., Local strong form meshless method on multiple Graphics Processing Units. Computer modeling in engineering & sciences. 2013;91:377-396; [26785063] :: manuscript
• Kosec G., Šarler B., H-adaptive local radial basis function collocation meshless method. Computers, materials & continua. 2011;26:227-253; [2177275] :: 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; [2024699] :: manuscript
• 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]