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15

As far as I know, Lapack is the only publicly available implementation of a number of algorithms (nonsymmetric dense eigensolver, pseudo-quadratic time symmetric eigensolver, fast Jacobi SVD). Most libraries that don't rely on BLAS+Lapack tend to support very primitive operations like matrix multiplication, LU factorization, and QR decomposition. Lapack ...

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If you want something open-source, you probably want to try COIN's CBC code (they also have a couple other MILP solvers, like a branch-and-price framework, or SYMPHONY). Gurobi and CPLEX will be considerably faster, and as of the 2011 or 2012 INFORMS meeting, Gurobi was faster than CPLEX (though the performance metrics are of course problem dependent). On ...

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If you want Matrix classes with an intuitive interface All the LAPACK and BLAS features Easy to learn and use API Easy to install Then I recommend you to have a look at my library FLENS. I designed it for exactly these kind of tasks. However, it requires a C++11 conform compiler (e.g. gcc 4.7 or clang). FLENS gives you exactly the same performance as ...

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I would say that there are a number of reasons why there are no computational science contests besides the potentially massive computational resources required. Time limits: Writing scientific computing code is usually not something that you want to rush. A lot of emphasis is on making sure it is correct, and thorough consideration of test/corner cases. ...

11

I maintain (and am the main coder of) a simulation software that has been developed for ~8 years and is used by few hundreds people. It all started as a side project during my PhD, and it clearly outgrew itself. It is both over- and under-engineered: the architecture of some parts is too complicated for their own good, whereas some other parts (whose ...

10

LibMesh supports Clough-Tocher and tensor product Hermite $C^1$ elements, see the biharmonic example. FEniCS has a biharmonic example that does uses a mixed continuous-discontinuous Galerkin formulation. Any package with $C^0$ elements that can compute second derivatives and can integrate DG jump terms can also use this approach. PetIGA Supports isogeometric ...

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I'll give you my perspective, which is encoded in the deal.II project that you reference. First, there are two kinds of error conditions: Errors that can be recovered from, and errors that can not be recovered from. The former is, for example, if an input file can't be read -- for example if you are reading information from a file such as $HOME/.dealii ... 9 Absolutely. You should check out VisIt, Paraview, Tecplot, Ensight, and similar tools. 9 In general, I'd say the following open source tools tend to be (roughly) best-of-breed, in the following order: PETSc has implemented a number of ODE solvers as part of TS, its time-stepping routines. There are a number of integrators implemented, including ARKIMEX, EIMEX, Rosenbrock-W, Crank-Nicolson, backward Euler, several Runge-Kutta methods (including ... 9 "developers lack the skills". Maybe. I think it's much more likely that the developers lack the incentives. Making solid code is difficult and expensive and, in academia, comes with minimal-to-negative reward. You're asking for a list of things of guidelines, but all of your examples are specific to the technical situation, not the social situation. That'... 8 the planned longevity of TeX comes to mind: “Ever since those beginnings in 1977, the TeX research project that I embarked on was driven by two major goals. The first goal was quality: we wanted to produce documents that were not just nice, but actually the best. (…) The second major goal was archival: to create systems that would be independent of ... 8 deal.II uses the Threading Building Blocks throughout the library and by and large we're reasonably happy with it. We've looked at a few alternatives, in particular OpenMP since everyone seems to be using that for simpler codes, but found them lacking. In particular, OpenMP has the huge disadvantage that its task model does not allow you to get a handle for ... 8 I would suggest that a full database may be overkill for your purposes, though it would certainly work. Even$5 \cdot 10^5$rows should be no more than around 25mb of data. I would strongly recommend doing the analysis/plotting/etc with the same tool that you will use for querying your data. It is my experience that when changing what to analyse only takes ... 8 You can try Geogebra (it is free). With SolveODE command and sliders you can do what yo want. For the usage of SolveODE command see. For example by using following command SolveODE[ <f'(x, y)>, <Start x>, <Start y>, <End x>, <Step> ] with SolveODE[A + B y + C sin(y), l, m, 10, 0.1] I got the solution curve below. You can vary ... 7 You might consider writing the entire paper in Noweb. It's a bit tedious to set up, but it's a very powerful way to mix code and LaTeX-formatted text, equations, and figures. For long programs, it tends to turn your code into more of a book than an article, but for short programs, it might work out pretty well. If you don't want to go that far, it still ... 7 The obvious answer would of course be to not implement it all yourself but to use what others have done before. For example, deal.II (http://www.dealii.org -- disclaimer: I am one of the authors of this library) already has DG elements on quads, hexes, and curved elements, tutorial programs that show how to use them, etc. All this has been tested for a ... 7 One of the authors of fenics, A. Logg, have written a very good paper on datastructures of storing meshes. The paper is A. Logg (2009). Efficient Representation of Computational Meshes http://arxiv.org/abs/1205.3081 In fact it's always a tradeoff between storing all the topological informations (nodes around nodes, faces around nodes, etc...) OR having to ... 7 Almost everything you can build and install in your own space. With GNU autotools, you can do something like ./configure --prefix=/path/to/your/work/space ... and then follow the usual compilation instructions. Things based on CMake and Scons have similar facilities. 7 Assuming that your kernel is somewhat smooth, use low-rank approximation. Here's a naive example: import numpy as np N=2000 input=np.random.random(N) x=np.linspace(-1,1,N) y=np.linspace(-2,2,N) X,Y=np.meshgrid(x,y,sparse=True) A = np.exp(1j*2*np.pi*X*Y) output = np.dot(A, input) U,S,V = np.linalg.svd(A) # find truncation rank for given tolerance k = ... 6 I use only two debuggers for serial and parallel programs: The Kernighan debugger, i.e. judicious print statements and careful thinking. Multiple instances of GDB as described o http://www.open-mpi.org/faq/?category=debugging#serial-debuggers. In the case where (2) is not sufficiently scalable, I refer to (1b). 6 (actually the comments provide an answer to your question, but this is additional information). 1) http://qblade.de.to/ This is a link to a free software called as QBlade. It is a wind turbine design and optimization software with emphasis on blade design (using XFOIL). This might come useful in designing/ optimization the rotor blades. What can it be ... 6 deal.II (see http://www.dealii.org/) does support Nedelec elements and, as a consequence, can solve the problems you're interested in. (Full disclaimer: I'm one of the principal developers of deal.II.) 6 There's no guarantee in the standard that any progress is made on the non-blocking sends until you actually call MPI_WAIT. It's a perfectly valid implementation to just queue up the operations and when you call MPI_WAIT, all of the MPI_ISEND operations complete at once. In reality, they usually tend to get a chance to progress anytime you enter the MPI ... 6 Mixed integer linear programming problems are much harder to solve than linear programming problems. In terms of computational complexity, LP's can be solved in polynomial time while solving MILP is an NP-Hard problem. The known algorithms for solving MILP's have exponential worst case complexity. There are other software packages for mixed integer ... 6 In deal.II, we basically only use vectors. Maps are too slow and scatter data all around memory, so we typically don't use them if the keys are integers and within a given range. For example, for the connectivity between cells, you can do arrays (STL vectors) in which you store neighbor indices and so that neighbor indices$4i\ldots 4i+3$correspond to cell$...

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All of the major finite element libraries (such as libMesh; FEniCS; or the project I run, deal.II) provide you with ready access to the system matrix and or any other matrices you need. They typically also have tutorials and examples from a wide variety of areas (e.g., structures, fluids, etc) that you can use to generate examples. Maybe a simpler first ...

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Why not give GMPY2 a try? From the introduction: gmpy2 is a C-coded Python extension module that supports multiple-precision arithmetic. gmpy2 is the successor to the original gmpy module. The gmpy module only supported the GMP multiple-precision library. gmpy2 adds support for the MPFR (correctly rounded real floating-point arithmetic) and MPC (correctly ...

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Even though I like Python as a language, distributing Python packages is a mess. I always find people not familiar with Python struggling with it. Next to the user-local install as outlined by Aron (using --user, or --prefix), another option is EasyBuild (http://hpcugent.github.com/easybuild/). Not only for Python packages, but for any (scientific) software ...

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The noweb approach mentioned by Bill has evolved quite a bit, both in it's original spirit of documenting code (rather than scientific publication) under the term literate programming and now comes in many flavors (I guess noweb was a generalization of cweb initially), of which doxygen and various language specific versions can generate documentation in TeX, ...

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The answer depends, in part, both on how robust of a solution you're looking for and on what kind of development workflow you use. One particularly simple option is to tag each cache entry with the version number of the software. As long as every change to the code is accompanied by a change in version number, this will give you an easy way to check whether ...

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