All Questions

1
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0answers
14 views

Computing any element of null space of singular matrix

Given a singular matrix $A$. What is the fastest method for finding a single non-zero solution to $Ax=0$. Note that we are NOT looking to find the whole kernel, we just want any non-zero vector in it. ...
0
votes
0answers
12 views

Time sampling changes solution

I'm currently trying to solve a problem using numerical methods. The set-up is rather long, so I apologize in advance... TL;DR: My solutions change depending on how big my steps are and I don't know ...
0
votes
0answers
16 views

Computational Biology [on hold]

Can people in SIS model can also be removed or die if the infection is fatal ? Consider a disease ’X’. People who are diagnosed in the earlier stage have high chance of recovery. But the intense ...
0
votes
0answers
14 views

state of art resources for transportation logistics

By transportation logistics, I mean the application of theoretical tools like traveling salesman problem, routing problem etc. So what are these applications? Well, stuff like how to schedule a fleet ...
1
vote
0answers
9 views

Nonlinear conjugate gradient with orthogonality constraint

I have to solve a set of nonlinear optimization problems in the subspace defined as the orthogonal space to a given vector. More precisely, $$ \arg\min f(\vec x) \qquad \text{with} \qquad \vec x \...
0
votes
0answers
11 views

Euler's method in scilab

I trying to solve this system of equations with Euler's method $$\begin{aligned} \frac{dn_0}{dt} &= -n_0(t)W_{01}(t) + n_1(t)K_{10}\\ \frac{dn_1}{dt} &= -n_1(t)W_{12}(t) - n_1(t)K_{10} + n_2(...
0
votes
0answers
11 views

How to start using python scripting in automotive power train? [on hold]

Looking for the basic things like what we can do with python in automotive.
0
votes
1answer
25 views

How to efficently plot a finite element mesh solution with matplotlib

I am looking for the most efficient way to plot a mesh using matplotlib given the following information, coordinates of each node, what nodes belong to each element, and the value each node has. Below ...
1
vote
1answer
29 views

Simplest way to precondition Uzawa iteration

I have a diffusion problem with an internal circular dirichlet constraint and a side condition which shall enforce a certain global volume integral. $\nabla(D \nabla u(x)) = 0$ outer boundary ...
0
votes
1answer
30 views

How to obtain linear tridiagonal system from PDE

I'm trying to re-solve the governing equations in hydraulic fracturing modeling as instructed step by step in a paper. After (A-9), the author stated that by substituting A-6, A-8 and A-9 into ...
1
vote
0answers
20 views

Solve ODE with non-negative and maximization constraints

My task is to solve $$\eta_k\frac{d^2C_k}{dz}(z)=-e_k, k = 1,2,3$$ $$C_k\ge0$$ $$C_1(0)=0, C_2(0)=A, C_3(0)=0$$ $$C_1(L)=B, \frac{dC_2}{dz}(L)=0, \frac{dC_3}{dz}(L)=0$$ with $$e_1 = -\beta_1-\beta_3$...
0
votes
1answer
35 views

CFL equation for non-linear equation

I am trying to solve numerically (obviously) inviscid Burgers' equation with the finite difference method. The equation is the following: $$ \displaystyle \partial_t u + u \, \partial_x u = 0 $$ ...
1
vote
1answer
31 views

Weak scaling for N-body simulations

I'm going to be doing some weak scaling of an $N$-body integrator on AWS. In the past when I've done weak scaling for this integrator I've fixed the number of particles per core ($N/n = {\rm const}$). ...
1
vote
1answer
24 views

How to obtain and form a 1st order differential equation for leapfrog integration from second order one in this example of coulomb drag

I am currently doing a computational physics homework which asked us to use leapfrog to give the relations between timevelocities and time-distance of these two objects. The full question is as ...
0
votes
0answers
39 views

Good C, C++ library for efficient grid search / tuples, ideally with bindings to Eigen

I have a $q$-dimensional grid, known at run, not compile-time, that has $50$ points in each direction and hence $50^3$ combinations that I would like to first build and then call a function with each ...
0
votes
0answers
20 views

How can I find the velocity of the capillary flow?

What is the best way of finding the capillary flow using computer vision? Procedure that I have been using so far: Selected a ROI Calculated the optical flow in the ROI to get a flow matrix ...
0
votes
0answers
4 views

VRP using or-tools with delivery constraints

I want to solve a vehicle routing problem where goods are collected from multiple locations, and then dropped at collection facilities. There are multiple collection points and they should be filled ...
1
vote
1answer
54 views

Is there a name for this integer linear optimization problem?

I have an integer linear programming problem of the form: $$\DeclareMathOperator{\tr}{tr} \min \tr WX$$ subject to: $$\begin{align} \sum_j X_{ij} < c_i && \forall i \\ \sum_i X_{ij} = 1 &...
0
votes
0answers
26 views

Finding second excited state of Schrödinger equation with secant Runge Kutta method

In our assignment, we are required to find the energies of the ground state and the first two excited states of the Schrödinger equation in a harmonic potential: $$V = \frac{50 x^2}{(10^{-11})^2}\, .$...
0
votes
1answer
23 views

How to improve the efficiency of periodicity detection for long time based lined and gapped datasets

Our data set has $10^4$ data points, but has a long baseline and many gaps. As the histogram shows, the horizontal-axis is time and most of the time, there are no data. The vertical-axis is data ...
0
votes
0answers
13 views

Numpy repeat for selected rows [on hold]

Is it possible to repeat selected rows in numpy? For example, can we get [[1, 2,3][1,2,3][4,5,6]] from[[1, 2,3][4,5,6]] ?
0
votes
0answers
21 views

extrapolation/interpolation in fmincg.m

Can you tell me these equations come from where in MATLAB fmincg.m? ...
4
votes
1answer
114 views

Is a symmetric bilinear form necessary to ensure a weak formulation has a solution?

Problem I want to convert the general second order linear PDE problem \begin{align} \begin{cases} a(x,y)\frac{\partial^2 u}{\partial x^2}+b(x,y) \frac{\partial^2 u}{\partial y^2} +c(x,y)\frac{\...
-1
votes
0answers
21 views

How to decrease the cost by direct computation of the jacobian given a system of equation with drift matrix

I have provided the R script of the project I´m working on.It works fine but computation of the required Jacobian at each step makes it costly. I need to find an alternate way to either compute the ...
1
vote
0answers
36 views

Properly sizing ParaView plots for LaTeX

I would like to make a visualization with ParaView for a paper. In order to have a high quality look, I would like the image to be, say, 300 dpi (or vector graphics). Moreover, since I know the column ...
0
votes
0answers
36 views

A fast way to check if a Matrix is ill-conditioned, and turning it into well-conditioned

I'm running a simulation, and some linear solvers are returning a message of ill-conditioned matrix. Hence, I'm looking for a fast, easy to implement, method to detect if a matrix is ill-conditioned, ...
-1
votes
0answers
15 views

Polyfit min/max constraints

I would like to "smooth" my prediction output and limit it to specific local min/max points. (The predicted line in blue - min is to low, how can I limit the polynomial equation accordingly?) My ...
1
vote
1answer
75 views

What's the minimum step size that can be used in Euler's method before it becomes unreliable?

In particular, if Euler's method is implemented on a computer, what's the minimum step size that can be used before rounding errors cause the Euler approximations to become completely unreliable? I ...
2
votes
1answer
79 views

Why the numerical solution of advection-dominant problem is challenging

In many CFD text books, usually there is a dedicated chapter for advection term discretization. Why discretization of such term in advection-dominated problems and near the discontinuities is ...
0
votes
0answers
28 views

Rigid FEM applicability for Viscoelastic Material

I have seen some scholars implement rigid FEM on viscoelastic materials, I would like to know whether this sound approach. In the following reference, they have implemented RFEM on viscoelastic ...
0
votes
0answers
50 views

Need help applying Implicit Eulers Method together with Newtons Method on Burgers' Equation

From the inviscid Burgers' equation: $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x} = 0$, I get the discretization $\frac{u_i^{n+1}-u_i^n}{\Delta t}+\frac{(u_i^{n+1})^2-(u_{i-1}^n)^2}{\...
1
vote
0answers
13 views

Instability in Lattice Boltzmann Solver

I wrote a Lattice Boltzmann Solver in Rust a little while back using both the BGK approximation and the TRT (two relaxation time) method on the D2Q9 lattice. In both cases I run into major stability ...
1
vote
1answer
114 views

How do I solve the matrix equality constrained optimization problem using Lagrangian multipliers?

Solve the following minimization problem in $\mathbf{X} \in \mathbb{R}^{m \times n}$ $$\begin{array}{ll} \text{minimize} & \frac 12 \| \mathbf{X}\mathbf{X}^T -\mathbf{A} \|^2_\mathcal{F}\\ \text{...
0
votes
0answers
15 views

Algorithmic recommendations for adaptive content suggestion [migrated]

I am interested in learning the ins and outs of adaptive content suggestion (similar to what facebook, google ads, youtube, netflix, linkedin and similar services typically do). I am new to the topic ...
3
votes
0answers
39 views

Use of non-typical values of $\theta$ in theta-methods

The theta-method is a popular solution for solving time-transient PDEs (or ODEs), which consists of solving the general equation for each time step: $$ \frac{u^{n+1} - u^{n}}{\Delta t} + (\theta f(u^{...
1
vote
1answer
18 views

Determine image of hypercube under linear map

Let $A$ be an $3\times N$ matrix (where $N$ is large) with nonnegative real entries. I'd like an algorithm for determining when a vector $v\in\Bbb R^3$ can be written as $Aw$ for some vector $w\in\Bbb ...
1
vote
3answers
92 views

Clustering with points lying along different 3D planes

I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit: There are roughly equal number of points lying along ...
0
votes
0answers
91 views

Matrix Equation Explained?

I am looking for some help on the equation below. I work as a programmer but I am self taught and have not studied Math at collage or university and this has left some holes in my education that I ...
0
votes
1answer
27 views

Optimize multivariable function with interdependent variables

I have a cost function with 2 parameters. The variables are dependent on each other. So, if I just take a partial derivative with respect to one variable the slope is in terms of the other variable ...
-1
votes
0answers
21 views

All root of a single complex nonlinear equation using MATLAB

Is there a built-in command or toolbox in MATLAB in order to find all roots of a single complex nonlinear equation? If not, what are the helpful methods to approach the problem with the least amount ...
1
vote
0answers
94 views

High-accuracy numerical differentiation

I have a $200 \times 200$ matrix representing the values taken by a function over an equally spaced grid. I would like to perform derivatives on it. I am interested in its gradient (i.e. its ...
3
votes
4answers
120 views

Numerical integration in Python with unknown constant

I’d like to solve the below equation for the unknown $T$: $$\int_0^\infty \frac{x^2}{\exp\left(\frac{x}{T}\right)-1}\kappa_x \mathrm{d}x = C,$$ where $C$ is a known constant and $\kappa_x$ is some ...
0
votes
0answers
39 views

Formulation of the least-squares parameter estimation problem

I have a system of 10 ordinary differential equations of the form, $\frac{dy_1}{dt} = f1(V1,k1,y1,y2)$ . . $\frac{dy_{10}}{dt} = f_{10}(V_{10},k_{10},y_{9},y_{10})$ I want to estimate the ...
5
votes
1answer
132 views

Advantages and disadvantages of space-time finite element methods

I have heard of space-time finite element methods. Although I was able to find some articles that describe the different possible methods from a mathematical point of view (thanks to Space-time finite ...
-1
votes
0answers
73 views

Finite Difference Method Algorithm

I'm trying to devise an algorithm for the finite difference method, but I'm a bit confused. The ODE in question is y''-5y'+10y = 10x, with y(0)=0 and y(1)=100. So I need a way to somehow obtain the ...
0
votes
1answer
56 views

Imposition of Dirichlet BC for Fourier pseudospectral in this paper

I was trying to implement the algorithm from the paper "Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh–Benard convection". I am having a hard time to ...
1
vote
1answer
338 views

What is the state of the art in solving stiff initial value problems?

I'm looking for current references on solving stiff ODEs. Most of what I know (say, BDF methods) apparently date back to the 1980's, and I feel like a lot of progress should have been made in that ...
0
votes
0answers
40 views

Avenues for application based research in network science for researchers from engineering departments

TL;DR: Is the field of network science ripe for engineering researchers? Network science has developed into a mature field for the study of complex systems. Huge amounts of works have been published ...
1
vote
1answer
100 views

Solving differential equation in Python with variable coefficients (I just know the coefficients numerically)

I am trying to implement a routine to solve a differential equation in Python. Basically the kind of equation that I am interested in solving is of the form: $\displaystyle \frac{d}{dx^2} \left(x y(x)...
0
votes
1answer
57 views

Error for the finite differences scheme — Advection equation

Consider the advection equation (1D in space) $$ \frac{\partial u}{\partial t} + V\, \frac{\partial u}{\partial x}=0 $$ and we solve it numerically on $[0,1]\times [0,1]\ni (t,x)$ using a forward ...

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