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4
votes
1answer
46 views

Sparse least squares with a (black-box) ill-conditioned operator

It was suggested on math.stackexchange.com that I try to ask this question here. Consider a bounded linear operator $A : U \to V$ where $U$ is finite dimensional and where $V$ is a separable Hilbert ...
0
votes
1answer
349 views

Proving solution existence and uniqueness of the Helmholtz equation with Robin boundary conditions with complex coefficients

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...
0
votes
0answers
27 views

Best method to solve this system of PDEs?

I have a system of PDEs constituting an initial value problem (IVP) consisting of three coupled PDEs: \begin{align} \partial_t \rho + \partial_x(\rho v) &= \left(k_A (1-\phi) + k_B \phi \right)...
0
votes
0answers
12 views

Finite volume method on a nonuniform grid

I would like to ask a question on the implementation of finite volume method on a non-uniform grid in solving Navier-Stokeq equations. I will just post the screenshot of a PhD thesis, where I found ...
1
vote
0answers
33 views

Calculating the cost function for numeric optimization (in MATLAB) of tuned mass damper

I am trying to implement a tuning strategy for a tuned mass damper (TMD) attached to a single-degree-of-freedom system. Here, we attach a secondary mass (TMD mass) $m_2$ to the primary mass $m_1$ by a ...
0
votes
0answers
11 views

Slow convergence of Stokes solver used with the Immersed Boundary method

I am using Immersed Boundary Method to simulate elastic particles in 3D Stokes flow. Specifically, one has $\nabla ^2 \mathbf{u}-\nabla p + \mathbf{f}(t) = 0$, $\nabla \cdot \mathbf{u} \; $, where $\...
0
votes
1answer
26 views

Scipy Find Peaks

I am trying to find the peaks. I have list x_period and y_power. I find the peaks from the ...
10
votes
4answers
32k views

Difference between Nodes and CPUs when running software on a cluster?

I'm looking into moving some computations of mine to a data center to get more computation power. In the context of this process, I am getting confused by the differentiation of a computation node and ...
3
votes
1answer
177 views

Time discretization Navier Stokes equation

This question is a follow-up of this one. The weak form of Navier Stokes equation is (assuming $v,q$ test functions for the velocity and the pressure, respectively) $$(\frac{du}{dt},v)_{\Omega} + (\...
0
votes
0answers
31 views

Mineral dissolution and solute transport around a solid

I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite). The governing equation for transport is the advection-diffusion equation, given as: ...
3
votes
0answers
29 views

How to troubleshoot numerical instability using finite difference for steady-state non-linear heat conduction equation

I have a problem which I believe is numerical instability when trying to solve a heat conduction equation using finite difference. The short version is that when the parameter $I=80.3$ I get the blue ...
-1
votes
0answers
21 views

VMD polymer draws multiple bonds [closed]

I'm new to VMD and I'm having some problems with displaying my polymer chain. Instead of just one bond, VMD draws multiple bonds. Why does this happen?
4
votes
0answers
46 views

Decomposing a banded matrix

Suppose we have a linear algebra problem with a banded matrix A which has nonzero entries on the main diagonal, two nearest sub-diagonals, and two other sub-diagonals (such band structure often arises ...
9
votes
1answer
361 views

Generalization of eigendecomposition problem

Let $A\in \mathbb{R}^{n\times n}$ and $v \in \mathbb{R}^n$. We recognize $Av=\lambda v$ for some scalar $\lambda$ as an eigendecomposition problem. Suppose $\mu \in \mathbb{R}^n$, and let $\odot$ ...
3
votes
3answers
111 views

Hypergeometric function $_2F_1(z)$ with $|z| > 1$ in GSL

I need to evaluate the hypergeometric function $_2F_1$ with $|z| > 1$ as in Wolfram Language with GSL but the GSL documentation says the $_2F_1$ needs $|z| < 1$. Is there any way I can use GSL ...
2
votes
0answers
78 views

How to position oneself, if one has little practical engineering background or function, but may have a broader insight into mathematical modeling?

How to position oneself, if one has little practical engineering background or function, but may have a broader insight into mathematical modeling? Or, lets say: I could write models to prove ...
0
votes
0answers
25 views

Find tuples of points from multiple sets

Given n sets of points in general position in dimension 2 (n typically small, 2-6), can one find tuples of points, one from each of the sets, which are close in some sense (the closest, mutual ...
0
votes
0answers
28 views

Can line search solve linear objective with nonlinear constraints?

Consider an optimization problem of the form: $$\max_{f(x)\le K,\\0\le x\le M} c^\top x,$$ where $f(x)$ is nonlinear. Can a line search of the following form be used to solve this problem? $$ \max_{\...
2
votes
2answers
370 views

Modelling question: example of a physical phenomenon with this jump condition at an interface?

in our finite element class we were talking about interface problems our teacher came up with the following, where $K_i$ are two given functions and $u_i$ is the restriction of the solution $u$ to $\...
2
votes
1answer
207 views

Integral image resizing

I'm trying to find an approach for integral image resizing. I found out that I can do it with a bilinear interpolation method, but with this approach I can only resizing by the factor which is a power ...
4
votes
1answer
447 views

Methods to implement floor dirt detection algorithm

I'm trying to detect dirty floor areas in a series of images, using MATLAB and its Image Processing Toolbox, like the one that follows: In the image above, there are two distinct areas, the whiter ...
7
votes
1answer
274 views

Robust smoothers for geometric multigrid

I'm searching for robust smoothers for geometric multigrids. By robust I mean: Effective for high order approximations (say spectral element, spectral Discontinuous Galerkin), Parallel (suitable for ...
0
votes
0answers
26 views

Restriction in (geometric) multigrid for vectors of non-even length

Naive restriction operators in geometric multigrid that I have seen are typically implemented as a convolution and a subsequent averaging of every two entries in a vector $v^h$. For example: $$\tilde{...
14
votes
4answers
2k views

What are some good strategies to test a floating point arithmetic implementation for double numbers?

For IEEE, the single representation is 1-bit sign, 8-bit exponent and 23-bit mantissa. This means that at each exponent value, you can test all 2^23-1 (roughly 9mil cases) possible combination of ...
11
votes
1answer
425 views

Increasing V-cycles for constant Coarsest Grid Size and increasing Fine Grid size

Problem statement I implemented geometric multigrid for $-\nabla^{2}=f$ where $f=\frac{3\pi^{2}}{4}sin \frac{\pi x}{2} sin \frac{\pi y}{2} sin \frac{\pi z}{2}$ on $\Omega \in [0,1]$ on a unit cube. ...
0
votes
0answers
31 views

Differences between Two-Grid Correction and V-Cycle Scheme

I found in A Multigrid Tutorial: Second Edition by William L. Briggs‏, Van Emden Henson‏, Steve F. (here) the following Schemes: Two-Grid Correction Scheme, p. 37: And V-Cycle Scheme, p. 40 I want ...
3
votes
1answer
108 views

Calculations on discontinous grids

Suppose for a grid-based calculation a grid is used such that the grid Jacobian is discontinuous. For example, in 1D, for a domain $x \in$ [0,1], one half of the domain is covered uniformly by twice ...
3
votes
0answers
51 views

Comparing block versus non-block Krylov methods for handling multiple right-hand-sides

Suppose I wish to solve a linear system $AX=B$ iteratively where $A$ is an $m\times m$ matrix and $X,B$ are $m \times s $ matrices (not single vectors). Instead of solving $s$ independent systems I'm ...
2
votes
1answer
49 views

How to stack N boxes of varying heights into M stacks, most evenly

The "standard" box-stacking algorithm(s) AFAIK assume a single stack and try to put the "largest" boxes on the bottom. The case I want to solve is simply to distribute the N boxes ...
6
votes
2answers
3k views

How to find the nearest/a near positive definite from a given matrix?

I'm given a matrix. How do I find the nearest (or a near) positive definite from it? The matrix can have complex eigenvalues, not be symmetric, etc. However, all its entries are real valued. The ...
4
votes
1answer
78 views

Worst Case complexity of a search engine algorithm

Computer make it possible to find information in large databases. However, the results are often too large to be returned in their entirety to the user who requests them. Computer therefore sort the ...
2
votes
0answers
85 views

Solve Rational Equation for Root Music in MATLAB

I'm trying to estimate DOA in the Hybrid architecture using root music so I need to solve the attached equation to find the roots for the Root_Music equation in Matlab. Does anyone have an idea for ...
4
votes
0answers
105 views

Any literature that extensively discusses the ability to strongly inter-/extrapolate computationally on little empirical data?

Any literature that extensively discusses the ability to strongly inter-/extrapolate computationally on little empirical data? This topic has fascinated me, but I find that it seems a bit novel. ...
0
votes
1answer
115 views

deal.ii - ParaView "warp by scalar" of my output is not continuous

During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in ...
11
votes
1answer
962 views

Numerical computation of Lyapunov exponent

I'm trying to compute the Lyapunov exponent for a smooth continuous time dynamical system(say, $\dot{\bar{x}} = f(\bar x)$). I using the QR decomposition method. Here are the steps that I follow. ...
-1
votes
0answers
47 views

Numerical scheme HJB equation

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...
7
votes
2answers
105 views

Approximating the boundary between two sets of points (in 2D): Fitting a region

Given two sets of points $p_{\text{in},i}$ and $p_{\text{out},j}$ inside and outside of what I intuitively call a "region", I would like to estimate and describe the boundary of this region. ...
0
votes
1answer
124 views

Specifying mesh spacing for DFT in numpy

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
7
votes
0answers
72 views

How do we approximate the numerical error a numerical scheme (e.g Runge Kutta, Euler etc) makes without having access to an analytical solution?

So I recently encountered this question in my head while taking my Scientific Computing class, where the lecturer talked about computing numerical error of a scheme. My guess would be that we take a ...
4
votes
1answer
144 views

Is there any way/any python function to calculate the condition number of the roots of a polynomial directly?

I know that NumPy has linalg.cond(A) to find the condition number of a matrix A. But, if I want to find the condition numbers of the roots of a large polynomial ...
0
votes
1answer
60 views

Finding total derivative of a multivariate function in Maple

In Maple, I have a function $f(x(t),y(t),t)$ that I want to differentiate with respect to $t$. I know the command for partial derivative $\frac{\partial f}{\partial x}$,$\frac{\partial f}{\partial y}$,...
1
vote
1answer
72 views

Can someone explain the equivalence between Oja's rule and PCA in a simple way?

I have to give a presentation on unsupervised learning in 2 days, and I have to explain/show the equivalence between Hebb's learning rule (or Oja's rule to be more specific) and PCA. The thing is that ...
2
votes
1answer
397 views

Suitable finite difference method for a convection-diffusion system?

I am trying to solve a system of PDEs $H_{t} = \frac{0.3}{0.7} - \frac{0.005 B f(h(H))}{\theta} - \frac{0.3 f(h(H))}{0.7} + \frac{500}{0.7} (HH_x)_x + (HH_y)_y$ $N_t = \frac{N_{in} - 0.002 [N] B f(h(...
2
votes
1answer
73 views

Elementary matrix of Raviart-Thomas elements

We can use the $RT0$ to solve the Darcy equation, i.e. $$k^{-1}\mathbf{u}+\nabla p = 0, \text{ in } \Omega,$$ $$-\nabla \cdot \mathbf{u} = 0, \text{ in } \Omega,$$ $$p = p_D \text{ on } \partial\Omega,...
-1
votes
0answers
35 views

Identifying Noetherian symmetries from general Lie symmetries of a differential equation

I know the Lie symmetry group of the harmonic oscillator differential equation from the literature. It is an 8 parameter Lie group. 5 of these generators generate Noether symmetry: $$G_1=\sin(2t)\frac{...
0
votes
0answers
55 views

Contact analysis does not converge due to the projection falls outside valid domain

I implemented Node-To-Surface contact algorithm (Wriggers, Peter, Computational contact mechanics., Berlin: Springer (ISBN 3-540-32608-1/hbk). xii, 518 p. (2006). ZBL1104.74002.). The code is done by ...
0
votes
0answers
25 views

How to use plot command in fenics [closed]

I'm new to Fenics and want to understand the plot command. My code: ...
12
votes
2answers
1k views

How do I find the minimum-area ellipse that encloses a set of points?

I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...
0
votes
0answers
48 views

Solve simultaneous differential equations with embedded functions and a parameter estimation

The aim is to solve the below equations and plot $m$ with time, i.e. $\frac{dm}{dt}$ $k$ is unknown and needs to be estimated. For the parameter estimation, the below values in the table for m versus ...
3
votes
2answers
137 views

Test functions of Raviart-Thomas elements?

The test functions of general finite elements are like interpolation functions (if my understanding is correct). But how about test functions of Raviart-Thomas elements? Let's raise the $RT0$ element ...

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