All Questions

4
votes
0answers
56 views

Fast approximate solver for vehicle routing problem

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...
29
votes
15answers
8k views

Good examples of “two is easy, three is hard” in computational sciences

I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows: When a certain problem is ...
2
votes
1answer
41 views

Time complexity analysis

I want to know the time complexity of following code Say I have a list unique_element[] There is an array which contain elements {4,5,2,4,7,8,1,5,9,8,1} Now as per my code I want to find out the ...
2
votes
0answers
33 views

How to determine the order of convergence of the Euler-Maruyama method?

This question is originally posted in Quant.StackExchange but has been unanswered for some time so I ask in here. To make this simple let us consider the Geometric Brownian Motions (GBM). My ...
1
vote
1answer
79 views

Dirichlet to Neumann Operator

EDIT: I am trying to specify my Question. Also I am not going to clearify which spaces I use, because I am only interested in the basic idea. I am looking at a standard elliptic second order PDE: \...
0
votes
0answers
9 views

XDMF version 3: how to describe uniform-grid image data?

I have the following, functional, XMDF file (version 2, or something like that) which I use to describe HDF5-stored heavy data for visualization in Paraview. I would like to upgrade to XDMF3 (just to ...
4
votes
2answers
98 views

Finite difference for a highly nonlinear equation - The wind within the forest

Based on the Navier-Stokes equations and a few parameterizations, the horizontal steady-state wind $u(z)$ within a forest of height H satisfies: $$ a\left(\frac{du}{dz}\right)^2 + b\frac{du}{dz} \...
1
vote
2answers
53 views

How to use MeshFunction in FEniCS (dolfin)?

I'm a beginner user of FEniCS and still struggling with some of the basics. Specifically, I have some issues doing the tutorials in the Langtangen-Logg book Solving PDEs in Python - The FEniCS ...
1
vote
0answers
32 views

Changing geometry scale breaks simulation

I'm trying to find the capacitance matrix for a small array of metal boxes in air using Comsol 5.4. The geometry presented here is a simple geometry that recreates the problem I'm experiencing. ...
1
vote
0answers
34 views

Stability of SVD, Eigendecompositions, and pseudoinverse procedures in modern LAPACK routines

I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways. One of these claims is that my proposed solution requires no explicit SVD and ...
2
votes
1answer
67 views

How to add extra constraints to a linear system for probabilities?

Background: I have an equation which looks like as follows: $W \times P = R$ $$\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \...
2
votes
1answer
65 views

How to justify using available code (in different language) for comparing algorithms

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...
1
vote
0answers
51 views

User friendly scipy optimize wrapper package?

I'm creating too much throw away code for interfacing with the scipy optimize package in a user friendly way. (See code below for example of interruptible optimization that keeps last optimization ...
0
votes
1answer
56 views

Dirichlet boundary conditions in the 1D Heat Equation

Please consider the assignment I have uploaded on the picture. I am confused about the functions $g_L(t)$, $g_R(t)$ and $\eta(x)$. What are they and how do I find them... My question: Is it possbile ...
-2
votes
1answer
80 views

How to plot 1/energy units in the energy (E) vs density of states (DOS) plot?

I have calculated the eigenvalues of Hamiltonian by exact diagonalization. Now I want to plot density of states (DOS) on y-axis and E on x-axis. DOS counts the number of energy levels in unit interval ...
1
vote
1answer
37 views

How to calculate the analytical solution of linear advection equation with Dirichlet's boundary conditions?

I am trying to find the solution of linear advection equation of the form: $\frac {\partial c}{\partial t}+u\frac {\partial c}{\partial x}=0$ $c(x,0)=0$ $c(0,t)=\{c_0 \ \text{for}\ t \leq t_1 \text{...
3
votes
2answers
77 views

Damped Harmonic Oscillation. Efficient algorithm to find the parameters resulting in threshold oscillation amplitude

Let's assume, that we have damped harmonic oscillation of a body in the form of a cone, immersed in a liquid. Equilibrium condition of the body is: $$m\overrightarrow{a} = \overrightarrow{F_\text{...
0
votes
1answer
139 views

Solving $n$ coupled equations numerically in Matlab

I would like to solve the following equations simultaneously and numerically for all $X, Y, Z, W$ where i = 1:Nw, j = 1:Nl, k = 1:K. $W_\text{net1}$, $W_\text{net2}...
0
votes
0answers
49 views

Solving a non-convex optimization problem using fmincon

I am trying to solve a non-convex optimization problem using fmincon(). At each iteration, I am iteratively looking for the optimum value and when the termination ...
0
votes
0answers
53 views

Is there a simple way of implementing dark energy into a n-body simulation?

I'm working on a gravitational n-body simulator and would like to implement dark energy into it but all I can find is papers with relativistic equations which I don't really understand. Is there a ...
0
votes
1answer
37 views

Animation using matplotlib

I am trying to animate a plot of two distinct points (blue and green points) moving about the complex unit circle using Python's Matplotlib library. The problem I am having is that the animation does ...
0
votes
1answer
26 views

PCJACOBI works but the default PCBJACOBI failed in PETSc

I am using PETSc and libmesh to solve a simple linear elastic problem with quite complicated geometry, using linear tetrahedral elements. I am always using the KSP CG as the solver. I noticed that ...
3
votes
1answer
76 views

Why would BFGS converge to a local minima of a non-convex function but maintain a large gradient?

I'm using BFGS to optimize a smooth but non-convex function $f$ that is computed by a simulation. The simulation also gives me a semi-analytical gradient $g$, which is verified by the numerical ...
0
votes
2answers
78 views

3d vs 2d finite element method

Is the theory of 3d finite element method just an assembly of 2d finite element analysis by putting planes on top of each other, or, a much more comple and different theory applies for 3d, with ...
4
votes
1answer
42 views

Definition of Lagrange nodes in Gmsh

When gmsh uses higher-order tetrahedral elements, there is an underlying Lagrange basis used to specify the map from reference space to the element. I'm trying to load a gmsh mesh of 3rd degree ...
2
votes
1answer
55 views

Rank of Hadamard Product with Masked Matrix

I have a matrix $A\in\{0,1\}^{d\times n}$ and $rank(A)=d,d<n$, and another matrix $X\in \mathbb{R}^{d\times n}$, but I do not know the rank of $X$. What can we say about the rank of their Hadamard ...
1
vote
1answer
65 views

Missing something fundamental about condition number estimation

In Higham's Accuracy and Stability of Numerical Algorithms, Chapter 15, algorithm 15.3 and 15.4: The topic is ostensibly condition number estimation, but these algorithms show how to compute $\gamma$ ...
2
votes
0answers
64 views

How can one prove the duality of Voronoi and Delaunay?

Hoping I'm not misunderstanding the concept here, but it is my understanding that Voronoi Diagrams and Delaunay Tesselations are 'dual' to one another, owing to the fact that each' solution makes ...
0
votes
1answer
106 views

Numerically solving a non-linear PDE

I have this non-linear partial differential equation. $$ \frac{\partial C}{\partial t}=\left(\frac{\partial C}{\partial x}\right)^2+C\frac{\partial^2 C}{\partial x^2} $$ I want to use the finite ...
0
votes
0answers
70 views

Double mach reflection at a inclined wedge

I am running into a strange problem when solving the 2D compressible Euler equations on a inclined wedge. To elaborate, my top boundary condition seems to emitting some type of instability. I have ...
0
votes
0answers
43 views

Augmented Lagrangian Techniques Frank-Wolfe Algorithm [python]

I'm trying to solve the convex quadratic problem (quadratic min cost flow problem) using the Frank-Wolfe algorithm. $$ \min\{x^TQx+qx: Ex=b,\quad 0\leq x \leq u\} $$ The standard algorithm is okay ...
0
votes
0answers
40 views

Singular Spectrum Analysis Explanation

I need you to help me understand the Singular Spectrum Analysis algorithm. I already read a lot of articles about the subject but they never answered my questions like what is the mathematical reason ...
2
votes
1answer
75 views

How to compute the determinant of Hessian of a multivariable function?

I have a function $F(\vec x)$ of many variables (let's say in the order of hundreds of thousands). I need to compute the determinant of the Hessian matrix at the point $x_0$. Is there a way to ...
0
votes
0answers
52 views

Bound for Expectation of Singular Value

In my case, $X_{\boldsymbol{\delta}}\in\mathbb{R}^{d\times M}$ is a function of Rademacher variables $\boldsymbol{\delta}\in\{1,-1\}^M$ with $\delta_i$ independent uniform random variables taking ...
3
votes
2answers
62 views

Convexity of Sum of $k$-smallest Eigenvalue

If I have a real positive definite matrix $A\in\mathbb{R}^{n\times n}$, and denote its eigenvalues as $\lambda_1\leq \lambda_2 \leq ... \leq \lambda_n $. Define the function as $f(A)=\sum_{i=1}^{k} \...
0
votes
1answer
79 views

Split-step Fourier method applied on Schrodinger equation

I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...
0
votes
1answer
54 views

Numerical Stability of a Generalized Spatial Discretization Scheme

After reading the matrix stability chapter (10) of Hirsch [1], I decided to dive in the reference list of the chapter. One of the papers [2], which is cited as reference shows an very interesting ...
0
votes
1answer
41 views

An Upper Bound of $\left<H,X\right>_F$ with Constrainted Rank

We have $X=[\mathbf{x}_1,\mathbf{x}_2...,\mathbf{x}_n]\in\mathbb{R}^{d\times n}$, $H=[\mathbf{h}_1,\mathbf{h}_2...,\mathbf{h}_n] \in\mathbb{R}^{d\times n}$, and $d<n$. $H$ has rank $r\leq d$ and $X$...
0
votes
0answers
39 views

Computationally obtaining the convergence rate of upwind scheme for Advection equation

The Advection equation (with velocity = 1) is $${\partial u \over \partial x} + {\partial u \over \partial t} = 0$$ I am trying to solve the equation with periodic BC. One of the ways to numerically ...
3
votes
0answers
47 views

Calculating depth mask from different lighting

I have a object which is static, the camera is static and light source is moving. How can the depth mask be calculated ? Concept is to use - calculate height from shadow length Lets imagine a have ...
0
votes
0answers
59 views

Quadrupole moment for a right triangle

The authors define a quadrupole moment for a right triangle in Lazić, Predrag, Hrvoje Štefančić, and Hrvoje Abraham. “The Robin Hood Method – A Novel Numerical Method for Electrostatic Problems ...
2
votes
1answer
66 views

Dormand–Prince 5(4): How to update the stepsize and make accept/reject decision?

https://en.wikipedia.org/wiki/Dormand–Prince_method I want to implement the Dormand-Prince 4(5) version to solve Initial Value problems. Using regular notation I have $A$ matrix and the $c,b,\hat{b}$ ...
2
votes
1answer
103 views

Why do we use hermite interpolation for finite element method in beams?

Why not just Lagrange polynomials basis functions
1
vote
2answers
39 views

denoting a variable as a matrix using octave syms package

I'd like to use the syms package to do some algebra for me, but the baseline assumption seems to be that variables are scalars. I would like to denote some variables as matrices. This will change the ...
0
votes
0answers
51 views

Writing python program for Weierstrass function with Monte Carlo

Our assignment asks us to create a python program to plot the Weierstrass function: Weierstrass function is an example of a pathological real-valued function on the real line. The function has the ...
0
votes
1answer
38 views

Monte Carlo - Random Walk Simulation - polyfit the log log data points?

This is part of the code in matlab for a random-walk simulation. To test the code, I'm using steps=[30]; there will be more values, but I want to run it for 1 trial to decrease code processing. <...
5
votes
2answers
108 views

Choose a subset of $m$ columns that maximize $|A^T A|$?

I have a set of $n$-dimensional vectors, and would like to choose $m$ of them to become the columns of an $n\times m$ matrix. I would like to choose the subset that maximizes $|A^T A|$, where $A^T$ is ...
0
votes
0answers
30 views

Extracting raw data from a graph

I am supposed to do black-box modeling, I need the input and output data for training, however, the authors didn't agree to share the raw data with me, I can only use their publication where these ...
1
vote
1answer
54 views

How to find a pair of divisors as close as possible to each other?

For a given integer $n\in\mathbb{N}^*$, I want to find a pair $(x,y)\in{\mathbb{N}^*}^2$ such that $x*y=n$ and $|y-x|$ is as small as possible. A naive algorithm I found is : ...
1
vote
1answer
96 views

(FEM) Reorder nodes or use sparse matrix storing techniques

Is it necessary to reorder nodes (using Reverse Cuthill-Mckee algorithm, for example) if I am already using a CSR or CSC storing technique? Because, since CSR/CSC only stores non-zero elements I guess ...

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