# All Questions

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### Estimation of time taken to reach steady state in an MD simulation of Poiseuille flow

I am trying to do a Molecular Dynamics Simulation of a complex fluid, confined between solid surfaces. I would like to find the flow rate as a function of fluid film thickness, $h$, for a plane ...
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### similarity/distance measurement between two ranked sequence

Is there an efficient way to measure similarity/distance between two sequences of ranked numbers/letters. The two sequences are of different length, and only have some elements in common? For ...
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### Quadrature order for finite elements and time dependent discontinuous Galerkin

When setting up a finite element system you have to use quadrature to calculate the integrals. I'm having trouble understanding what order rule to use. I know of some rules of thumb, for example with ...
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### Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation

My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
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### Reference request for matlab

I am a complete beginner in computing and I am trying to learn some computing skills. I am learning how to use Matlab as my first programming language. Are there are websites that have notes for ...
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### On the flight/matrix free SVD of large sparse matrix

I am trying to apply SVD to large sparse matrices. I already compared the performances of Propack and irlba to those of the matlab svd and svds. These two packages enhance significantly the computing ...
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### What is the best way to stop an asynchronous-heterogeneous MPI program?

I want to stop immediately an MPI program, that has N processors and each processor runs a different program (with different computational complexities). Processors share information to each other ...
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### Comparison between of higher order interpolations

A while ago I came up with an algorithm which can be used to numerically solve optimal control problems, which basically came down to discretizing the control input $u(t)$ and interpolating this to ...
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### CAS Problem with integrals

I got this problem thrown at me, unfortunately I lack context at the moment but I thought Maple or Mathematica would solve it anyways. I have a function $f$ over $x$ and $y$ such as this (Maple) ...
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### adjoint method package for ODE(PDE)-constrained optimization

I have this type of question (ODE-constrained optimization) to solve: $g(x,p)=0$ is the simulation, where $x$ is state variable and $p$ is parameters aimed to optimize; $f(x)$ is the objective ...
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### bifurcation diagram MATLAB runs out of memory

I have a 3000 x 2301 matrix 'xfinfin' in MATLAB that I want to plot in the following way: ...
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### CFL Neccessary Condition

The theorem states that if a difference scheme converges then it necessarily satisfies the CFL condition. How can this be proved?
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### Manipulating/Extracting Data and Developing Methods - Language Choice [on hold]

As a general programming enthusiast and aspiring Bioinformatician student I have an intermediate understanding of computing (languages) as well as Java, and to a lesser extent C++. Having knowledge in ...
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### Solving an ODE using shooting method

I have been trying to solve the following nonlinear ordinary differential equation: $$-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0$$ with boundary conditions ...
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### Multigrid on “not perfectly rectangular” grid

Multigrid introductions normally use a rectangular grid. Interpolation of values is then straight forward: Just interpolate linearly on the edge between two adjacent nodes of the coarse grid to find ...
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### Laplace Operator with PyNFFT

I am learning to use PyNFFT for nonuniform FFT. I try to apply the laplace operator to functions. As a test, I want to take $f(x) = \cos( 2\pi i k \cdot x)$, calcualte (using the package) $\Delta f$ ...
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### Test of 3rd-order vs 4th-order symplectic integrator with strange result

In my answer to a question on MSE regarding a 2D Hamiltonian physics simulation, I have suggested using a higher-order symplectic integrator. Then I thought it might be a good idea to demonstrate the ...
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### Ill-conditioned Jacobian matrix from Nernst-Planck equation with Butler-Volmer reactions

The governing equations are listed here of my notes on page 4. It's a reproduction of other's paper which solves the equations with COMSOL. The problems arise when I want to solve for the consistent ...
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### What's the role of visualization?

I'm just starting at scientific computing and I'm seeing that results can be generated merely by plotting the variables. Of course more variables lead to more axes/dimensions so e.g. a three variable ...
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### Building minimization optimization problem for 2nd-order elliptic PDE

I am solving elliptic PDE problem, for which, Euler scheme looks as following: $$\nabla [\gamma ( |\nabla u|^2) \nabla u] = 0,$$ where $$\gamma(|\nabla u|^2) = (1 + |\nabla u|^2)^{-1/2}.$$ I am ...
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### Optimal partitioning of a graph

Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
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### Diffrence between moving least square and weighted least square in interpolation

Could you explain exact difference between moving least square (MLS) and weighted least square (WLS). I personally feel that moving least square is a sub case of weighted least square. My ...
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### FENICS subdomains - restriction/ prolongation operators

I am trying to implement my own multigrid method in fenics. Is there any "smart/ fenics" way how to assemble subdomains and obtain restriction/ prolongation operators ? Thanks!
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### Use scipy to get any vertex of polytope

I need to get just a random vertex of a polytope. Any will do. The only way I can do this now is to pick a random function (say 0s) to maximize with scipy.optimize.linprog. However, this is wasteful, ...
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### Inverted value is not consistent with expectation

We have a group of observations $$y = f(x_1, x_2, x_3) \enspace .$$ We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of ...

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