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599 views

Tensor notation in fenics [closed]

Within Fenics what ordering is used for storing vectors as upper triangular matrices? Th:e question really is I define a green Lagrange strain tensor in the following way: ...
1
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0answers
93 views

Minimizing a quadratic form

I would like to minimize the following quadratic form: $$ f(\mathbf{\theta}) = (\mathbf{y} - \mathbf{\mu}(\mathbf{\theta}))^T \mathbf{\Sigma}({\mathbf{\theta}})^{-1} (\mathbf{y} - \mathbf{\mu}(\mathbf{...
1
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0answers
484 views

How to solve nonlinear optimization with constraints that have singular jacobian

I'm solving a nonlinear constrained optimization with constraint of following form: $$\mathbf{A}^T\mathbf{A}-\mathbf{I}=\mathbf{0}, \mathbf{B}^T\mathbf{B}-\mathbf{I}=\mathbf{0}$$ where $\mathbf{A}$ ...
1
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0answers
1k views

COMSOL - 2D box - get for every x an average value over y (line average apply for more lines) [closed]

I would like to ask you for your help. I have 2D box. I know how to do an 2D cut line and compute an average value of someting over this line. (in Results -> Data Sets -> Cut Line 2D and then Results-...
1
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0answers
100 views

Stability question (finite difference): dealing with corner nodes

Consider one initial boundary value problem for sphere. $$\frac{\partial u}{\partial t}=\operatorname{div}A\nabla u +f$$ Here is explicit numerical scheme (we consider that it is stable): $$\frac{u^{...
1
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0answers
54 views

Calculating the number of molecules diffusing out of a volume [closed]

I have a system of reactions that are governed by differential equations. They are reacting inside of a volume with known dimensions i.e lbh. I don't have any other information on their position ...
1
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0answers
188 views

Is it possible to generalize the two view Sampson error to multiple view cases in computer vision?

In multiple view geometry of computer vision, there is a geometric error called Sampson error which is very useful in the nonlinear estimation of fundamental matrix....
1
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0answers
133 views

Quadratic programming problem involving permutation matrices

Does anyone know a good algorithm for quickly finding an approximate solution to the following problem? Given two square matrices $A$ and $B$, minimize $\| P A P^\top - B \|$ over all permutation ...
1
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1answer
1k views

Lid driven cavity flow problem to solve with the help of projection method and use coding in fortran 90 [closed]

I want to solve Lid driven cavity flow with the help of projection method i want to make own fortran program to solve two dimensional unsteady flow. I propose to solve the equations in the following ...
1
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0answers
43 views

how to find outward normal for robin codition [duplicate]

I wrote the code to fix this problem; now I should validate it using a test function to see the error in my code. I can't figure out how starting from u can derive the function g on the edge, in ...
1
vote
1answer
293 views

Ray tracer : create an uniform grid [closed]

I wrote a simple ray tracer, and now I try to implement an uniform grid. There is a lot of documentation on how to traverse the grid, but I don't know how to construct the grid. I have my uniform ...
1
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0answers
211 views

Characteristic length of differential element of cylinder surface?

I am trying to find the Nusselt number for a small element of the outside of a cylinder that has a height of $\Delta z$. I found the average Grashof number of a surface as $$Gr_{L}=\frac{\beta \rho (...
1
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0answers
190 views

Problem with cell size and boundary conditions in transient cylindrical conduction

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as ...
1
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0answers
51 views

Size reduction of matrices in dispersion curve calculation

I have an energy dispersion curve obtained from the eigenvalues of $$E(k) = \text{eig}(T e^{ik} + T^H e^{-ik} + H_0),$$ where $H_0$ and $T$ are $N\times N$ square matrices, $T^H$ is the Hermitian ...
1
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0answers
87 views

Increase convergence of non-linear equations resulting from ODEs

I am trying to solve a set of couple ODEs: $V_l(r) - r W_l(r) - f1(r) W_l' = 0\tag 1$ $r^2 h''_l(r) + f2 r h_l'(r) + f3 h_l(r) - f4 U_l(r) = 0 \tag 2$ $\kappa (U_l + h_l) + V_{l+1} + W_{l+1} = 0\...
1
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0answers
339 views

Image processing problems that can be solved using parallel computing? [closed]

Many of the problems in Image processing are embaressingly parallel. But I want to know is it worth solving Image processing using parallel computing? Are there real practical problems in image ...
1
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0answers
85 views

Prove $T_n(x)$ of Chebyshev Polynomial given the recurrence relation [closed]

Using the recursion formula for Chebyshev polynomials, show that $T_n(x)$ can be written as $$T_n(x)=2^{n-1}(x-x_1)(x-x_2)...(x-x_n)$$ where $x_i$ are the $n$ roots of $T_n$ The recurrence relation:...
1
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0answers
179 views

How can i find the coordination number with voro++? [closed]

Could anybody please help with voro++ cause i am new to this software?My problem is how can i find the coordination number of an atom ,cause i checked it for a bcc lattice and it gave me 24 for all ...
1
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0answers
352 views

Practical implementation of spatial binning for rectangular range queries

I have a bunch of polygons and a coarse uniform grid. I want to implement two different range queries, for a rectangle aligned with the uniform grid: Does the rectangle intersect with any polygon at ...
1
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0answers
75 views

Will Sumatra interfere with git?

As far as I understand, Sumatra does some sort of versioning of simulation scripts and output files. If I start to use Sumatra inside a git working directory, can Sumatra end up interfering with git ...
1
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0answers
1k views

Crank-Nicolson for 2nd- and 4th-order finite differences

I modeled the heat equation, $$ u_t = au_{xx} $$ using the common 2nd-order Crank-Nicolson scheme, $$ \frac{u^{n+1}_i-u^{n}_i}{dt} = \frac{a}{2\,dx}\left(u_{i-1}^{n+1}+u_{i+1}^{n+1}-2u_i^{n+1} + u_{i-...
1
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0answers
216 views

Numerically evaluate 1D inhomogeneous wave equation solution

I am trying to solve the following 1D inhomogeneous wave equation. Forgive me if I a miss any rigorous mathematical concept. $$ \frac{\partial^2 u}{\partial x^2} - \frac{1}{c^2}\frac{\partial^2 u}{\...
1
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0answers
88 views

Assignment optimization problem

I have to find a solution to a problem and I don't know where to start. Lets imagine I have a list of n containers and m processes. Each process resides already within a container and have 4 ...
1
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0answers
111 views

Recursive-Multiply Analysis [closed]

I am not sure if I can post these kinds of questions on this site, but I was wondering if you could help me with a question that's been bothering me. We have started learning about analysis of ...
1
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0answers
108 views

Quadratic optimization without any cross terms

I need to solve a quadratic program in Java which minimizes a sum of squares. The problem is that there are constraints to be satisfied, and so a quadratic optimizer must be used. I've been thinking ...
1
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0answers
42 views

Spectra of the energy flux VS transfer spectra?

In direct numerical simulation of turbulence what is the advantage to look at the spectra of the energy flux rather than the transfer spectra? The transfer spectra corresponds to the triple-velocity ...
1
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0answers
83 views

Issues with CVX package for optimization

I am trying to use the cvx package for optimization. However, I am having some issues with it. I have a variable X which is a matrix but I cannot add $X^{-1}$ in the objective function. What should I ...
1
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0answers
55 views

Malliavin Derivative with Mathematica is it possible? [closed]

From mathematica.stackexchange: Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form $$F=F(\...
1
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0answers
62 views

speckle interferometry (or other interferometry) software

This might not be the best place to ask, and if its not could someone please point me to where would be better, but here we go anyway. Does anyone out there know of open source software which can be ...
1
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0answers
20 views

Reduction for NP-hardness [duplicate]

Consider the following optimization problem: \begin{align} \text{Min}_{i\neq j\neq s\neq t} |x_i x_j-x_sx_t|\\ s.t: Ax=b\\ x\geq 0; \end{align} This problem can be seen as an instance of non convex ...
1
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0answers
259 views

Curvature of level-sets of CG1 function

Let us have simplicial mesh and continuous function $u$ which is piece-wise linear and non-constant on every cell. Then normal vector to level-sets of $u$ is given $$\mathbf{n}=\frac{\nabla u}{|\nabla ...
1
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0answers
62 views

discrete versions of Lp norm

The discrete analogue of the $L_p$ norm for the mesh function $V$ is $$\|V\|_{l^p(\bar{\Omega}^N)}=\left(\sum_{i=0}^NV_i^p\bar{h}_i\right)^{1/p}$$ where $\bar{\Omega}^N$ is an arbitrary mesh, $\bar{h}...
1
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0answers
2k views

Simulink PDE (MATLAB)

I need to build a system in Simulink that solves a PDE, but I can't find any literature or books where it is described how to do it (especially any stuff according to modeling PDE in Simulink). ...
1
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0answers
108 views

Hatree-Fock, reasons for convergence/ non-convergence

I'm new here so please forgive me if I lack proper stack exchange etiquette. So, I was wondering if anyone here could provide insight on a problem that I am running into with with a Hartree-Fock ...
1
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0answers
236 views

Block Backward Differentiation Formula (BBDF), on order 4 formula

I am trying to implement a program the numerical method to solve ODE called Block BDF as explained in this article: https://waset.org/journals/waset/v38/v38-49.pdf As it is variable step-size, I need ...
1
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0answers
55 views

Sine series using exponential based FFT

I have such a problem - I would need to expand a discrete function in a sine fourier series but I would like to use exponential based library for FFT (I will use CUDA to compute it). What have I to do ...
1
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0answers
30 views

Combining trend estimation and constrained Marquart fit

This title certainly needs some clarification: I need to compute parameters $a_i$ for a helper function $f(\vec{a};k)$ (for grid interpolation) which is fitted to a number of values $y_k$ which are ...
1
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0answers
266 views

Accurate force-field for MD

I am still a fairly new graduate student, and I am having trouble simulating a metal-organic framework. I am currently using UFF (I implemented it for LAMMPS), and it works well for some MOFs, but ...
1
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0answers
37 views

Simulation of asymmetric structures (occupancy = 0.5) unstable

I am trying to simulate a metal-organic framework in LAMMPS using the UFF potential. It's working quite well for some structures where all molecules have an occupancy of 1. However, when I have a ...
1
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0answers
66 views

Looking for a java library or algorithm for efficiently implementing the second Chebyshev function

Does anyone know of a java library or algorithm for efficiently implementing the second Chebyshev function? To be clear, I'm refering to this expression: $$\vartheta(x) = \sum_{p \le x}\log p$$ $$\...
1
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0answers
490 views

CUDA Mandelbrot Set effective bandwidth and optimization

I was reading through this article (very good article and excellent blog BTW) to do some measurements in my (very simple) implementation of the Mandelbrot Set. I'm using a Quadro 2000D card which has ...
1
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0answers
85 views

How to create synthetic data from known weights

I'm doing some machine learning where I have lots of data and through optimization I'm trying to learn the weights for the model. I'd like to check that my learning actually works correctly. For that ...
1
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0answers
223 views

Sign or cardinality constraint when solving for sparse signal

I'm currently learning about using linear and semidefinite programming to find sparse solutions to problems. In particular, finding sparse solutions where the sampling functions are sinusoidal (...
1
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0answers
364 views

features recognition & reconstruction of 3d mesh delaunay matlab

I managed to display the coordinates of x,y and z into a 3D mesh by using delaunay function. The coordinates are in .obj format actually and i have read it into matrix form. Now, i would like to ...
1
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0answers
1k views

Pixel-To-Angle Transformation in Camera Image

I'm trying to localize points I see in a camera image in terms of azimuth and elevation and match points between shots. Individual shots should differ only in rotation around the camera's center (...
1
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0answers
63 views

Can I use RANS to see the effect of mixed convection?

my question is: can I use a RANS simulation to see the effect of mixed/natural convection? Actually I have also a second question: I would like to do this in Comsol multiphysics, but it seems that it ...
1
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0answers
266 views

Memory allocation error with GSL ODE solver applied to system of 4 ODEs

I am trying to solve a (large) system of ODEs with GSL solvers. When I use driver method I get an error message of could not allocate space for gsl_interp_accel, ...
1
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0answers
155 views

What libraries are available for solving problems at the college physics level? [closed]

Are there any libraries available for solving problems at the level of college physics? In particular, I'm interested in libraries for general purpose programming languages that can calculate results ...
1
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0answers
98 views

Modified heat eq. in 3D [closed]

please how can I write gradient numerically? I have an eq. $\dfrac{\partial X}{\partial t}=\nabla^2 X + u\nabla X$ I wonder how write this in 3D. Many thanks for any idea... I can find how to solve ...
1
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0answers
28 views

PCA performed on a configuration with scaled axes

Suppose a configuration $X\in\mathbb{R}^{n\times 2}$ is output of PCA on some high-dimensional data $Y\in\mathbb{R}^{n\times h}$. Note that this PCA is performed by $$X=Y\cdot U,$$ where columns of $U$...

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