All Questions

0
votes
1answer
47 views

Combining multiple coupled 1st order equations in python

I'm having serious troubles with solving translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline ...
0
votes
1answer
49 views

Imposing zero mean condition in FEM

I wanted to solve a periodic elliptic equation of the form $$-\nabla\cdot(A\nabla u)=-\nabla\cdot F$$ on $Y=[0,2\pi)^d$ using FreeFem++, where $A$ and $F$ are $Y$-periodic. The space of solutions is $...
0
votes
0answers
25 views

Determine endpoint of a graph given as a list of nodes + direct successors and predecessors [migrated]

I fix a type T once for all. (Concretely, T is a c# class, but that doesn't matter.) On T I have the notion of direct successor ...
-1
votes
0answers
16 views

How to distinguish different cracks/enriched regions in Abaqus from UDMGINI subroutine?

I want to use different failure criteria for two or more separate enriched regions in one model. The regions are always in different instances made from different materials. I've tried to get ...
0
votes
1answer
16 views

Minimize squared error of linear function

Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the ...
0
votes
0answers
27 views

Minimizing the ratio of two specific non negative quadratic convex functions

$F$ is $m\times m$ diagonal, with real non negative elements $D$ is $n \times m$ complex $P$ is $n \times 1$ complex $A$ is $m \times 1$ complex. Minimize $\Gamma(A)$, with respect to $A$. $$\...
1
vote
1answer
109 views

Do there exist “frameworks” as to how computational scientific experiments claim validity? Scientific method for computed science?

Do there exist "frameworks" as to how computational scientific experiments claim validity? Like "scientific method for computed science"?
-1
votes
0answers
23 views

implementing custom force laws in OpenFOAM

How can I implement a custom force law (e.g., Van der Waals's forces) in OpenFOAM? I am new to OpenFOAM.
2
votes
2answers
67 views

projective reconstruction from orthogonal views

This is a problem from projective geometry. Suppose I have a vector $z \in R^k$ of unit length $\| z \| =1$ inside a $k$-dimensional hypercube. I don't know its value but do know its projection upto ...
1
vote
0answers
63 views

PDE discretization on triangular domain

Given the 2D Poisson equation $$\Delta u = f\\ u(x,0) = g_1(x), 0<x<1\\u(0,y) = g_2(y), 0<y<1\\ \partial_n u (x, 1-x) =0, 0<x<1$$ defined on the domain $\Omega := \{(x,y) \in \...
0
votes
1answer
29 views

TMZ TME modes, clarification

I'm refering here to Taflove's "computational electrodynamcis, 3rd ed." He says Let us assume that the structure being modeled extends to infinity in the z-direction with no change in the shape ...
0
votes
1answer
45 views

Discretization Neumann boundary condition

I'm currently working with the following Poisson equation with mixed boundary conditions, including a Neumann boundary condition. $$\Delta u = f\\ u(x,0) = g_1(x), 0<x<1\\u(0,y) = g_2(y), 0<...
2
votes
1answer
82 views

Is there an optimization scheme/algorithm that converges, for this non-convex scenario but with some special properties

I have a smooth function $f(x) = \frac{g(x)}{h(x)}$ that is the ratio of two smooth convex functions $g(x)$ and $h(x)$. It is known that $f(x)$ has a global minimum, achieved at the unique point $x_0$....
-1
votes
0answers
22 views

Tracking fluid movement in a pipe

I have a general question regarding developing an algorithm for a problem that has come up. I need to track fluids of different densities as they travel down a pipe in a well, then come back again to ...
2
votes
0answers
37 views

Open source multiphysics software that can model the interaction of two insulators with a user-specified electrical force law?

Given two solid bodies of masses $m_1$ and $m_2$ with invariable charge distributions $\rho_1(\mathbf{r_1})$ and $\rho_2(\mathbf{r_2})$ in them,* respectively, I would like to model the electrical ...
0
votes
0answers
34 views

OpenCV: How to get the “rectified” fundamental matrix?

I have a stereo image pair and the respective intrinsics and extrinsics of both cameras. With this information, I can calculate the fundamental Matrix between the two cameras (let's call it F). I can ...
0
votes
0answers
41 views

How does one do electrodynamics simulations in SU2?

The description of SU2 says The primary applications are computational fluid dynamics and aerodynamic shape optimization, but has been extended to treat more general equations such as ...
3
votes
1answer
65 views

Smoothness regularisation of a 2D field on a triangular mesh?

I'm working on an inverse problem where the solution is the values of a 2D scalar field at the vertices of a 2D triangular mesh, such that the field can be defined continuously inside the mesh via ...
1
vote
0answers
48 views

Finite Element Model of Euler-Bernoulli Beam Theory with Isoparametric Element

In the formulation of Euler-Bernoulli Beam Theory, there are two degrees of freedom at a point, $w$ and $\frac{dw}{dx}$. Typically, the finite element model of this theory uses cubic polynomial for ...
1
vote
0answers
45 views

Simplification of an optimization objective

Let $G(V,E)$ is a weighted simple graph, where $V$ and $E$ are the set of vertices and Edges. The graph is undirected. Let $A \in \{0,1\}^{n\times n}$ and $W \in R_+^{n\times n}$ be the adjacency ...
0
votes
1answer
33 views

Vehicle Route assignment with capacity constraint

Problem Background I'm trying to find a solution/model to the following problem: Let's consider a cellular network (mobile network, ie., hexagonal cells) denoted $N$ composed of $|N|$ cells. Each ...
1
vote
1answer
24 views

Research articles on MultiObjective Non-Linear Programming (MONLP)

I'm looking for papers dealing with multi-objective non-linear programming which could help me implement an algorithm to solve my problem. My problem is : Maximize $f(x) = c \cdot x$, while ...
0
votes
0answers
32 views

Open Source Packages Implementing Continuous Wavelet and Scaling Functions

I'm looking for an open source software package that provides a fast evaluation of continuous Daubechies/Symmlet wavelet/scaling functions. GSL only has the discrete wavelets, and PyWavelets comes ...
0
votes
1answer
56 views

Finding Matrix inverse with LU and repeted left division calls

Hello I am in a basic numerical methods class and our teacher has given us an algorithm which can compute the inverse of a matrix other than using MATLAB's built in library function. ...
1
vote
0answers
33 views

Number of $S_n$-orbits in $P^k(\{1,\dots,n\})$

This is a particular case of a question I asked on Mathematics Stackexchange, question which got no answer so far. Let $n$ and $k$ be integers with $n\ge1$, $k\ge0$, and let $a(n,k)$ be the number of ...
3
votes
3answers
125 views

Simple way to store/read data from file in C++

I've been running various simulations with C++, and doing so has often involved saving lots of data to file (real/complex matrices, arrays, etc) and then reading them into other programs later. ...
0
votes
0answers
55 views

Determination of Jacobian when there are more than 1 degrees of freedom at a node

In finite element method, the formula for Jacobian is $ J =\beta^T X$ where, $\beta = [\frac{\partial N}{\partial \xi} \frac{\partial N}{\partial \eta}]$ and $X = [x_1 y_1; x_2 y_2; .. x_n y_n]$. ...
6
votes
2answers
232 views

Is Highams' computation of mean worth the price?

In Accuracy and Stability of Numerical Algorithms, equation 1.6a, Higham gives the following update formula for the mean: $$ M_{1} := x_1, \quad M_{k+1} := M_{k} + \frac{x_k - M_k}{k} $$ Ok, one ...
1
vote
1answer
33 views

Minimizing the used memory in diffusion simulation using Python

I am recently dealing with a diffusion simulation project and I have come up with the following code: ...
3
votes
2answers
49 views

Finding exact rational solution to linear integer equations in Matlab

I have a linear system of equations $$Ax=b$$ where $A$ is an $N\times N$ matrix with integer values, and $b$ is a $N\times 1$ vector with integer values. Due to prior knowledge, I know that I am ...
2
votes
1answer
110 views

A robust algorithm to sort a non-convex polygon vertices

Let v_{0},...,v_{N-1} be N points in a Cartesian xy plane defining the vertices of closed polygon (i.e. v_{N} = v_{0}). Let P_{0}...
1
vote
1answer
22 views

Domain transformation squashing interior quadrature nodes into boundary

In many quadrature problems, we are interested in computing $\int_a^b f(x) \, \mathrm{d}x$ via a quadrature sum. However, most software packages precompute the quadrature nodes and weights for use ...
1
vote
0answers
16 views

Piecewise-linear Continuations vs Marching Squares/Cubes

It seems that both piecewise-linear continuation and marching squares are methods to produce iso-contours of a scalar function given the function's values on a grid. It seems that piecwise-linear ...
0
votes
1answer
41 views

How to reorder/cluster adjacency matrix to maximize the interaction along the super diagonal?

I have the following code which takes a DataFrame and plot the pdist matrix. ...
0
votes
1answer
39 views

Node re-numbering in 1D mesh GMSH

I'm working with Gmsh to generate 1D meshes of polygon edges. I have noticed that drawing a polygon by "vertices and lines" the program always assigns to the first N nodes of the mesh the coordinates ...
2
votes
0answers
61 views

Numerical analysis, pivoting and incomplete LU decomposition

When doing LU decomposition, the algorithm will break down if any of the diagonal element $x_{ii}$ is zero. Therefore, we can use pivoting on the matrix such that $x_{ii}$ is no longer zero. That is ...
0
votes
0answers
55 views

How to add red noise to a CFD simulation?

I am using a piece of code to simulate magnetohydrodynamics (MHD). I would like to drive waves on the boundary of my domain. I can drive sinusoidal waves easily by simply specifying: $$v = v_0\sin(\...
1
vote
1answer
121 views

Normalization of polynomials for discontinuous Galerkin methods (DGM)

I was curious if someone could share their opinion on this matter. I have noticed that some people in literature normalize their Legendre polynomials, i.e. divide or multiply the polynomial by $$\...
0
votes
1answer
61 views

Unexpected solutions solving an ODE using odeint

I am trying to solve a system of 8 coupled differential equations using scipy's odeint. I have already written my code and it runs fine, but the solutions I get are completely different from what I ...
6
votes
1answer
105 views

numerical solution of an under-determined linear equation in high dimensions

I need to solve a linear regression problem $$Ax=y$$ which is hugely underdetermined. I have around $10^6$ features but only $10^3$ equations. So $A$ is a $1,000\times 1,000,000$ matrix and $y$ a ...
3
votes
1answer
47 views

Numerical solving Lotka-Volterra ODE in R

Aim: I am trying to numerically solve a Lotka-Volterra ODE in R, using de sde.sim() function in the sde package. I would like to use the ...
2
votes
1answer
100 views

Projection onto the set of Orthogonal matrices

Let $M \in \mathbb{R}^{n \times n}$ and denote the set of Orthogonal matrices by \begin{equation} \mathcal{O}_{n} = \left\lbrace Q \in \mathbb{R}^{n \times n} \colon QQ^{T} = \mathbb{I}_{n} \right\...
0
votes
1answer
47 views

How can I coarsen a mesh in Gmsh when 'Mesh options' include 'Refine by splitting' but nothing about coarsening?

I am new to Gmsh and I am having trouble creating a circle with a coarse mesh. I use Geometry->Elementary entities->Add->Circle to create the geometry ...
1
vote
0answers
62 views

How to solve potential flow with FEM, stream function, and the Kutta condition?

I'm trying to solve two-dimensional potential flow over airfoils with the finite element method, using the stream function formulation ($\Delta\psi = 0$, $u = -\partial\psi/\partial y$, $v = \partial\...
0
votes
1answer
61 views

Load the mesh file with boundary marks

I'm want to load a mesh from a file, generated by triangle, and I want to use the boundary marks of its nodes (boundary marks of the file). It is possible? Also, I can change the mesh generator (or ...
2
votes
1answer
65 views

Eigenvectors associated to two quasi-degenerate eigenvalues

I need to find the smallest eigenvalue and the corresponding eigenvector of a sparse matrix $M$ whose dimension is $\approx 10^4$. Within Matlab enviroment, I use the command ...
2
votes
2answers
95 views

Asymptotic Complexity of Gaussian Elimination using Complete Pivoting

I would like to know the algorithm asymptotic complexity with Complete Pivoting. With partial pivoting, it is known to be $O(n^3)$. Is it the same for complete pivoting?
1
vote
0answers
59 views

SDE solver in python: manual determination of integrator step size (dt)

Aim: I am trying to solve a system of SDEs, while using the SDEint package in python 3.x. It is a system of SDEs adapted from and inspired by the Zombie Apocalypse ...
0
votes
0answers
25 views

Compute a Boltzman partition function

I'm trying to calculate total energy of a system $$ E(v, h) = -\sum a_iv_i - \sum b_jh_j - \sum_{i,j} v_ih_jw_{ij} $$ Python equivalent looks like this ...
1
vote
1answer
73 views

Conjugate gradient - ill-conditioning and numerical tolerance

I would like to solve system $Ax=b$, where $A$ is SPD, but very ill-conditioned ($\text{cond}(A)>10^{11}$). I am interested in using UNpreconditioned version of the conjugate gradient method. Is ...

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