### Anders Loggowner

Examples - New demo generated with development branch logg/topic-multimesh

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New demo generated with development branch logg/topic-multimesh

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Finite element PDE peeps -- FEniCS (http://fenicsproject.org/) is now in https://cloud.sagemath.com. See http://ask.sagemath.org/question/3506/can-fenics-be-setup-on-sagemath-cloud?answer=4644#4644

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So Sage has FE capability now? It'll soon actually be all-in-one scientific computation suite, I guess.

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Please take a moment to complete the FEniCS user survey at https://docs.google.com/forms/d/1bcs2Jwv9pZ8J57rLIUjZBj8BD-_tcUiU11NGX9VkWAs/viewform

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+Florian Rathgeber I suggested a C++/Python question too, but was also too late. Something for next time.

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+Kristian Ølgaard successfully defended is PhD thesis at TU Delft on 3 December 2013. His thesis is available at http://dx.doi.org/10.4233/uuid:9c703850-e7fd-457c-a94a-ce0c0af27c0d. Amongst other things, the thesis describes in the detail the optimisations that are employed by FFC when generating quadrature-based code.

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Now accepted for publication in Computational Science & Discovery: "What makes computational open source software libraries successful?"

www.math.tamu.edu/~bangerth/publications/2013-software.pdf

Of all the papers I've written, this was the one that got more personal reactions from the reviewers than any other. It's also the one that I put the most heart into. (Thanks, +Timo Heister for making it happen!)

www.math.tamu.edu/~bangerth/publications/2013-software.pdf

Of all the papers I've written, this was the one that got more personal reactions from the reviewers than any other. It's also the one that I put the most heart into. (Thanks, +Timo Heister for making it happen!)

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The fenicstools package is available on https://github.com/mikaem/fenicstools/wiki. The package was developed primarily because of an interesting problem faced when our simulations were becoming larger on remote clusters, whereas our laptops were still relatively small. We could run simulations, but not visualize our results! With fenicstools it is possible to slice up (or use 3D boxes) any geometry and store these slices to vtk-files. A simulation of cerebrospinal fluid illustrates this nicely. The simulation used 30 million elements divided up between approximately 100 compute cores. The figure below shows the velocity magnitude in slices throughout the spine.

In addition to visualization, the package also contains a parallel routine for interpolation on non-mathcing meshes and routines for sampling turbulence statistics.

In addition to visualization, the package also contains a parallel routine for interpolation on non-mathcing meshes and routines for sampling turbulence statistics.

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Sorry, I have no experience with remote rendering. I've always done simulations on a cluster and visualizations on my laptop, which is exactly why I needed fenicstools in the first place!

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Simulation of injection molding flow with immersed fibers. The Folgar-Tucker equation was solved with quadratic closure approximation.

The fiber orientation at each point is shown (eigenvector scaled by the (eigenvalue-1/2) of the fiber orientation tensor with largest eigenvalue).

Other videos (Navier-Stokes Phase field) in my channel:

http://www.youtube.com/user/feosp

The fiber orientation at each point is shown (eigenvector scaled by the (eigenvalue-1/2) of the fiber orientation tensor with largest eigenvalue).

Other videos (Navier-Stokes Phase field) in my channel:

http://www.youtube.com/user/feosp

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Sneak peak at a very preliminary version of a FEniCS GUI developed by +Nina Kristine Kylstad who has been working as a summer intern at Simula this summer. Great job!

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The FEniCS Project is a collection of free software with an extensive list of features for automated, efficient solution of differential equations.

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Registration and abstract submission for the FEniCS’14 Workshop in Paris (16 and 17 June) is now open. See http://fenicsproject.org/featured/2014/fenics14_paris.html for details.

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Paper describing UFL has appeared in ACM Transactions on Mathematical Software (also on arXiv, http://arxiv.org/abs/1211.4047)

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FEniCS components are now in MacPorts thanks to +Sean Farley .

Done! After many years of tedious work SciencePorts is no part of MacPorts!

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FEniCS release 1.3 is out! Source tarballs are available for download and binaries will be available in the next few days.

Release has many performance and installation improvements.

Release has many performance and installation improvements.

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Examples of block preconditioning for Stokes-like problems with DOLFIN using the PETSc FieldSplit functionality can be found at https://bitbucket.org/magma-dynamics/preconditioning. The code is C++ only at present. Once the interface has evolved, a Python version will become available. The example code is supporting material for the paper http://arxiv.org/abs/1311.6372.

A number of changes will soon be made in DOLFIN to make the application of block preconditioners simpler and more efficient.

A number of changes will soon be made in DOLFIN to make the application of block preconditioners simpler and more efficient.

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Manufactured solutions for the heat equation

I have compiled a python module that is ready to be used to check numerical routines, in particular time integration schemes or linear solvers, by means of manufactored solutions.

It considers the heat equation, takes a sympy expression as analytical solution, provides the stiffness and mass matrix from FEniCS as scipy sparse matrices, and it comes with methods to retrieve the current (in time) source term, analytical solution, and the approximation error.

Feel free to check it out from mit github account. There is also a link to the documentation.

https://github.com/highlando/manufacsols-4-heateqn

I have compiled a python module that is ready to be used to check numerical routines, in particular time integration schemes or linear solvers, by means of manufactored solutions.

It considers the heat equation, takes a sympy expression as analytical solution, provides the stiffness and mass matrix from FEniCS as scipy sparse matrices, and it comes with methods to retrieve the current (in time) source term, analytical solution, and the approximation error.

Feel free to check it out from mit github account. There is also a link to the documentation.

https://github.com/highlando/manufacsols-4-heateqn

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I use the export to scipy's arrays to employ custom time integration schemes or linear solvers.

I agree that what sympy does here, can also be done by FEniCS. Though sympy might be more powerful for symbolic manipulations. So, the sympy integration is not necessary but, maybe, convenient (for people that are not familiar with the ufl).

I agree that what sympy does here, can also be done by FEniCS. Though sympy might be more powerful for symbolic manipulations. So, the sympy integration is not necessary but, maybe, convenient (for people that are not familiar with the ufl).

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In the DOLFIN development version, Armadillo has been replaced by Eigen3 (http://eigen.tuxfamily.org/, https://bitbucket.org/eigen/eigen) for dense linear algebra. The documentation, syntax, range of functionality and performance of Eigen are all very impressive.

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The degree-of-freedom ordering in DOLFIN was never guaranteed, but some users built code that depended on a particular ordering. The ordering was changed in a recent DOLFIN release. Some numbers showing the dramatic speed-up that can be achieved, and which motivated the ordering change, have been posted at http://fenicsproject.org/pipermail/fenics/2013-September/000556.html.

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Loads of previously undocumented DOLFIN demos have now been documented. Check out the new documentation at http://fenicsproject.org/documentation/dolfin/dev/python/demo/index.html

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We now have a twitter feed for FEniCS news at @fenicsnews. News items will also appear on the FEniCS web page at http://fenicsproject.org.

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Numerical modelling of advection problems is always beset with difficulties, especially from numerical diffusion. Here, we have been working on a "flux limiter" for advection equations on the RT1-DG0 basis.

The advected quantity is discretised on DG0, but the advection uses a higher order (DG1) representation to calculate fluxes. Normally, this would introduce spurious oscillations, but by limiting the gradient, this is avoided. Net result: reduced diffusion, 100% conservative and obeys max-min principle. The images below show the same calculation (a buoyancy driven flow) at the same time step, one using a simple upwind method (right), and the other the flux-limited method (left).

The advected quantity is discretised on DG0, but the advection uses a higher order (DG1) representation to calculate fluxes. Normally, this would introduce spurious oscillations, but by limiting the gradient, this is avoided. Net result: reduced diffusion, 100% conservative and obeys max-min principle. The images below show the same calculation (a buoyancy driven flow) at the same time step, one using a simple upwind method (right), and the other the flux-limited method (left).

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I'm going to be working on this more in the future - so I'll keep you posted... it is not very sophisticated at the moment, but if you want to have a look at my bitbucket repository, I can add you...

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