# All Questions

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### Exploring feasible points in a linearly defined space

What is the quickest way to find a point inside a linear feasible space? (Defined by the intersection of several hyperplanes and halfspaces). I want to be able to choose an initial point in the ...
1k views

### Best practice for storing hierarchical simulation data

TL,DR What is the accepted best practice in scientific computing circles for storing large quantities of hierarchically structured data? For example, SQL does not play nicely with large sparse ...
229 views

### CFD for high-detailed turbulence and non-linear waves

What are typical (or promising) techniques and methods in CFD to achieve high-detailed turbulence and non-linear waves interaction? And with "active" geometry (when bodies interacts with fluid in both ...
1k views

### What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?

I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR: cell refinement criteria determine a list of ...
978 views

### Approximate spectrum of a large matrix

I want to compute the spectrum (all the eigenvalues) of a large sparse matrix (hundreds of thousands of rows). This is hard. I am willing to settle for an approximation. Are there approximation ...
1k views

### eigenvalues (and determinant) of a hadamard product of matrices

I need to compute the determinant of a matrix that is calculated as $B \circ A$, with $B$ and $A$ being square matrices and $\circ$ representing their Hadamard product. One way of doing this is ...
1k views

### SVD for finding the largest eigenvalue of a 50x50 matrix — am I wasting significant amounts of time?

I've got a program that computes the largest eigenvalue of many real symmetric 50x50 matrices by performing singular-value decompositions on all of them. The SVD is a bottleneck in the program. Are ...
1k views

### f2py: error f90 not supported by GnuFCompiler needed for source_file.f90

I'm trying to install a Python package that relies on extensions built from Fortran 90 using f2py, but I get the following error: ...
307 views

### Computing Permanents of $64 \times 64$ Matrices

I need to compute the Matrix Permanents of several $64 \times 64$, zero-one matrices. I have tried using the built in functions in both Sage and Maple, but both programs return out of memory errors. I ...
569 views

### What algorithm for solving a set of stiff ODEs would be easiest to port to high precision floating point arithmetic?

I want to solve a relatively small system of stiff ODEs (< 10 first-order equations) using high precision floating point arithmetic (using MPFR or alike). What would be the easiest algorithm to ...
3k views

### Drawbacks of Newton-Raphson approximation with approximate numerical derivative

Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
261 views

### efficiently solving a low rank linear parametric systems?

I have a large number of systems of the form: $Ax=b_i$ To solve for a large numbers of such $b_i\;1\leq i \leq k$ but where $A$ is fixed (A is a rank $p$ general --i.e. non sparse, non PSD-- ...
212 views

### Different kinds of Integral Equation Methods

I am relatively new to integral equations for solving time-harmonic EM scattering problems. I have read a decent number of papers on the subject, and it seems that for formulations that can support 3D ...
386 views

### Get equation for a curve which intersects x at seemingly randomly distributed points?

Is there any type of function that when graphed would show a curve which intersects the x axis multiple times, with each point being an arbitrary distance from the last? I mean, not like a trig ...
9k views

### Interpolate 2D data

I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an ...
8k views

### Is there an in practice limit on the number of constraints on a linear programming problem?

I am new to linear programming and have formulated a linear program (LP) with order of $10^{13}$ variables and $10^{13}$ constraints, although the constraint matrix is extremely sparse. I wanted to ...
1k views

### How to numerically calculate residues?

I need to calculate the following integral: $${1\over 2\pi i} \int_C f(E) \, d E$$ $$f(E) = {\rm Tr}\,\left(({\bf h} + E)\,{\bf G}(E) \right)$$ Where $\bf h$ is a matrix (one particle kinetic and ...
786 views

### How to handle large numbers of output data sets from a simulation/sensitivity analysis?

Somewhat related, but I think the question is distinct enough to justify a separate question. As a bit of background, I come from a observational/statistical Epidemiology background, working with ...
855 views

### How do I make sure that the results of my simulations and the results in my paper are always in sync?

In one of my papers, I list some numerical results in addition to some figures. What I'd like to do is make sure that the numerical results in my paper always agree with the code. Right now, I just ...
4k views

### Specifying boundary conditions for imported mesh in OpenFOAM

I have a mesh produced from scanning a real 3D object (I don't have a geometry). What is the most convenient way to specify inlets, outlets, etc. for CFD in OpenFOAM? The mesh consists of thousands of ...
3k views

### How do I know if my code is being vectorized by the compiler?

As exemplified by Jed Brown's answer to Costs of lookups versus calculations, using vectorized vs non-vectorized floating point operations results in much faster code. Many modern compilers claim ...
794 views

2k views

### Newton-based methods in optimization vs. solving systems of nonlinear equations

I asked for clarification about a recent question about minpack, and got the following comment: Any system of equations is equivalent to an optimization problem, which is why Newton-based methods ...
389 views

### How to add back integral constraints to linear program solution

I am implementing a machine learning algorithm for which I need to solve an integer linear program. To get the solution in polynomial time, the authors of the algorithm have dropped the integral ...