All Questions

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 ...

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 bodies' ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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. ...

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 ...

I have an ODE with the initial condition: $y'=2r\sqrt{y}$, $y(r=0)=1$. I am thinking of using either Forward-Euler method or Leap-Frog to solve this numerically. However before I implement a ...

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. ...

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 $X = [x_1 y_1; x_2 y_2; .. x_n y_n]$. ...

I am trying to write a MATLAB program for solving a plate problem using Classical Plate Theory. I am using rectangular 4 noded element with 3 degrees of freedom on each node, $w$, $\frac{\partial w}{\...

Hello I have an equation in that is in the form of a string: for example: 2n+5h+19q-6=15j+16a+17a+5 Is there an easy way to move all the variables and coefficients to the left side and the constants ...

I'm working on a project that requires n-body simulation in real time, and with the barnes-hut implementation I'm able to get around 1500 particles with a reasonable framerate, but I'm really looking ...

I am new to finite element and deal.ii library. I am using the finite element method for my research and going through the tutorials of deal.ii library. A deal.ii example has a grid generated like ...

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 ...

I am recently dealing with a diffusion simulation project and I have come up with the following code: ...

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 ...

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}...

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 ...

I've implemented code to find the solution to the discretisation of the following PDE: $$\tau_V \frac{\partial V}{\partial t} = E-V + \lambda^2 \frac{\partial^2 V}{\partial x^2} + i_\text{app}$$ ...

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 ...

Can I move onto fields like computational biology or computational neuroscience after taking a PhD in Computer Science?

I have the following code which takes a DataFrame and plot the pdist matrix. ...

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 ...

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 ...

I learning AMBER for bio molecular simulations. Apart from the AMBERs official tutorials and manual, I have not able to locate some book which guides a beginner into using AMBER proficiently. Are ...

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(\...

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 $$\...

How can I put a constraint x^H * x >= a ? x and a are a vector.

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 ...

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 ...

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 ...

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\...

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 ...

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\...

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 ...

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 ...

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?

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 ...

The social force model is a model using Newtonian forces to describe the movement of individuals. As seen page 1 Each individual feels the following forces: A driving force towards the goal $$ m_i\...

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 ...

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 ...

I saw some definition that if $$M=\max_{x\not=0} \tfrac{\|Ax\|}{\|x\|} \quad\text{and}\quad m=\min_{x\not=0} \tfrac{\|Ax\|}{\|x\|} \,,$$ the condition number of $A=M/m$. In my opinion, If we have a ...

I'm a software engineer and I've just started to fly rc-planes. I'm currently building a self learning auto-pilot for my plane and I'm really interested in CFD. I installed OpenFOAM and ran through ...

I want to preprocess a relatively large dataset using python. I implemented some Dask parallelization and was stunned by the time reduction. I figure there are other libraries or frameworks I could ...