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1500 questions
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5 answers

Computing the Voronoi diagram of a region inside a box

I am facing a problem as follows: I have a box full of points with a certain unknown distribution and I would like to calculate its Voronoï Diagram. The problem is that the number of points is so huge that this may be impossible to do for the full…
ccorbella
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Is the sparsity pattern of a linear system important for iterative (KSP) solvers?

Pretty much the question. Given a general sparse, non-symmetric (both numerically and structurally) matrix, how important is the sparsity pattern (i.e. row/column permutation of matrix/vector) for iterative solvers? I can see it becomes important…
mmirzadeh
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structured grid and unstructured grid

I am new to the field of CFD. When should one go for structured grid and when should one go for unstructured? (Yes, it depends a lot on the geometry of the problem) More specifically, I want to know the difference in the computational power…
Subodh
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What does Python offer for distributed/parallel/GPU computing?

Using the SciPy/NumPy libraries, Python is a pretty cool and performing platform for scientific computing. I just wonder: When I have to go parallel (multi-thread, multi-core, multi-node, gpu), what does Python offer? I'm mostly looking for…
Michael
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Solving non-linear singular ODE with SciPy odeint / ODEPACK

I want to solve the Lane-Emden isothermal equation [PDF, eq. 15.2.9] $$\frac{d^2 \!\psi}{d \xi^2} + \frac{2}{\xi} \frac{d \psi}{d \xi} = e^{-\psi}$$ with the initial conditions $$\psi(\xi = 0) = 0 \quad \left.\frac{d\psi}{d \xi}\right|_{\xi = 0} =…
astrojuanlu
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Solving shifted linear systems with LU factorization

I am interested in solving a sequence of shifted linear systems $(A+\sigma I)x = b$ for various values of $\sigma$. The matrix $A$ is sparse and not too large, so I have its LU factorization available. What is the best way to do this? This is for…
Victor Liu
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Tucker factorisation to compare multiple PCA decompositions?

This is an entry-level question for multiway matrix decompositions. I have a set/population $k$ of entities (here biological cells) for each of which I also have a number ($l$) of flavours of length $N$ vectors (genetic-like measurements for which…
drw
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What is too big for standard linear algebra/optimization methods?

Different numerical linear algebra and numerical optimization methods have different size regimes where they're a 'good idea', in addition to their own properties. For example, for very large optimization problems, gradient, stochastic gradient and…
cjordan1
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Taxonomy of ILU preconditioners

I learned that for BiCGStab solver for sparse linear systems it's pretty much always necessary to use a preconditioner. I realized by now that choosing a good one is problem dependent. Surfing the web I found out there are many ILU based…
Johntra Volta
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When is it advantageous to iterate integrals numerically?

If there is an $(n+1)$-dimensional integral of the form $$ \int_{[0,1]^{n+1}} f(x, y)\,\mathrm{d}^n x \,\mathrm{d}y,$$ normally one would evaluate this using a multi-dimensional integration library over the whole domain, $[0,1]^{n+1}$. But are there…
Kirill
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Why does conjugate gradient work with this nonsymmetric preconditioner?

In this previous thread the following multiplicative way to combine symmetric preconditioners $P_1$ and $P_2$ for the symmetric system $Ax=b$ was suggested: \begin{align} P_\text{combo}^{-1} :=& P_1^{-1} + P_2^{-1}(I - A P_1^{-1})\\ =&P_1^{-1} +…
Nick Alger
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Minimizing a quadratic function with nonlinear constraints

what would be good methods (and/or software packages) to try for solving a problem minimizing a quadratic function $f(x) = \sum_{i=1}^N{(x_i - y_i)^2}$, s.t. $0 \leq x_i \leq 1$, and there are more constraints some of which are non-linear (and…
laxxy
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Finite difference scheme for compressible nonisothermal flow in porous media

My challenge is to solve the following system of equations, which describe gas combustion in porous media: 1) Continuity $\varepsilon \frac{\partial \rho_g}{\partial t} +\frac{\partial}{\partial x} \left(\rho_g u_x\right)=0$ 2) Darcy law…
tiam
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Anyone knows references summarizing the history of supercomputing?

Anyone knows references summarizing the history and ideas behind supercomputing including mentioning of developments in parallel programming languages, applications, startup companies (some was establish but didn't survive), needs of industry, etc.
Allan P. Engsig-Karup
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How can I precondition a non-linear problem before linearization?

When I think of solving non-linear equations, I generally think of linearizing first, then applying a preconditioner to the linear matrix. The thought occurred to me that it might be possible to condition the non-linear equations BEFORE they are…
Paul
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