# Tag Info

16

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 ...

16

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 ...

11

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

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 ... 10 "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'... 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 ... 8 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 ... 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 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 ... 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 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). 7 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$...

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 = ...

7

You can calculate GFLOP rates this way, but the numbers are pretty meaningless on today's hardware: Floating point operations require a variable number of clock cycles. An addition is generally cheaper than a multiplication, but each generally takes more than one clock cycle of the 2.8 billion cycles you quite. When you have hyperthreading, you have two ...

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

If you want to try a bunch of different solvers, give Julia's JuMP modeling framework a try. It lets you write your model as a JuMP model, and then switch out the solvers with one line of code. For example, for MILP problems you can choose from the Bonmin, Cbc, Couenne, CPLEX, GLPK, Gurobi, and MOSEK solvers. Because of this, if you write it in JuMP, you can ...

6

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 ...

6

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 ...

5

gmsh is a viable way to generate quadrilateral meshes in 2d. It's also open source.

5

Permit me to clarify - you ask about "structured mesh" that's "quadrilateral." By definition, a structured mesh (or grid) consists of quads (2D) and hexes (3D). So I want to clarify that you're inquiring about automatic structured quad/hex grid generation. If so, you're seeking the holy grail. While there are many software tools for generating structured ...

5

For my work, I tend to have programs output a sequence of still images, and I then convert them to an animated format in a post-processing step. To make a video, I use ffmpeg (http://www.ffmpeg.org/); to make a .gif, I use imagemagick (http://www.imagemagick.org/). Both of these tools are easy to script from the command line. There are numerous tutorials ...

5

I highly recommend using a tool such as Sumatra for this. I used to have a similar "pedestrian" approach to yours for keeping track of many simulation runs with varying parameters, but in the end it just becomes a huge mess because it's next to impossible to design such an ad-hoc approach correctly upfront and to anticipate all the use cases and extensions ...

5

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It depends on how quad precision is implemented. If you want to implement it as "traditional" floating point numbers with sign, mantissa, and exponent (the latter two just having more than the normal 53 and 10 bits of double precision), then doing this on a processor that doesn't natively support it, is going to be pretty expensive because it will involve a ...

5

If you just want the computational results and aren't running benchmarking tests then this isn't a serious problem. If you're trying to benchmark the performance of the code and get repeatable run times for comparisons with a an alternate version of the code, then this can be an issue.

5

Here is a simple (Matlab) Newton method as a first attempt to help get started. It finds 1087 roots with error below $10^{-11}$. f = @(x) ((2*x)./(x.^2-1)) - tan(x); fp = @(x)-tan(x).^2+2.0./(x.^2-1.0)-x.^2.*1.0./(x.^2-1.0).^2.*4.0-1.0; x0 = 0; for jj = 1 : 1200 %number of iterations to find some roots x0 = x0 + (jj-1)*(jj/10^4); %take previous ...

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