All Questions

Filter by
Sorted by
Tagged with
1
vote
0answers
42 views

A problem with Poisson equation

I'm computing the Hartree potentials of atoms by solving the Poisson equation and I use hydrogen atom as a test case. The Poisson equation for hydrogen atom in atomic units is given by $$\nabla^2 V_H =...
0
votes
0answers
10 views

How to calculate skewness for a mesh?

I am writing a code to calculate mesh quality stats such as: cell volume, face areas and non-orthogonality between faces (basically something like OpenFOAM's ...
2
votes
1answer
760 views

Local truncation error of Dufort Frankel Scheme

The scheme is given by $$\frac{v_m^{n+1}-v_m^{n-1}}{2k} + b\frac{v_m^{n+1}+v_m^{n-1}-v_{m-1}^n-v_{m+1}^n}{h^2} = 0$$ where $v_m^n$ is the numerical solution at the $m^\text{th}$ spatial coordinate ...
-1
votes
1answer
27 views

Dealing with arrays and fit function in Gnuplot

I want to evaluate the Birch-Murnaghan Equation of State (BM-EOS) for different volumes. I tried declaring a 1D array A in which every element would be the answer ...
0
votes
1answer
19 views

Effecient method for iterating over sparse dataset

Apologies if this isn't the appropriate forum for this question. I have a set of elements that I need to iterate over as part of a modeling workflow. The elements exists over a set of dimensions (i, ...
-1
votes
0answers
14 views

Solving an LPP using the simplex method and given a basic feasible solution(corner point) to start with

I want to solve an LPP using the simplex method. I am also given a corner point to start with. I don't understand how do I construct the initial tableau that corresponds the given corner point? I will ...
0
votes
0answers
18 views

Computing Womersley number

I'd like to know whether the blood flow is pulsatile in small capillaries present in tissues that lie away from the heart. From the literature, I understand that the Womersley number can be computed ...
0
votes
1answer
176 views

Elliptic PDE finite volume method with Dirichlet boundary condition

I want to discretize the following equation using a Finite Volume Method $$\nabla \cdot (a(x)\nabla u)=f(x)\\x\in \Omega \subset \mathbb{R}^2 \\u_{|\partial\Omega}=g$$ I'm using Voronoi cells here: ...
0
votes
0answers
21 views

Understanding STRUCTURED_POINTS dataset in VTK

Based on my readings this is what I have gathered: Dimensions: Number of data points in the x, y, z directions Spacing: Space between points in each dimension Origin: Location of origin Cell data: ...
0
votes
1answer
357 views

How to make a less diffusive code to solve 2D advection equation?

I would like to solve the following differential equation numerically in 2D, $$\frac{\partial z^-}{\partial t}+(\vec{B}\cdot\vec{\nabla})z^-=0,$$ see Wikipedia if you are curious about what the ...
2
votes
1answer
235 views

Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
-1
votes
0answers
15 views

Computational power comparison

Is there any way to meaningfully compare the computational power of our best computers to the computational power of the human brain? And if the answer is yes then which system has the upper hand?
0
votes
1answer
29 views

Getting streamline for a lid driven cavity flow in openFoam/ParaView

I have installed openFoam on Debian GNU/Linux and learning from official user guide. I have a problem with generating streamlines. I am trying to generate streamlines as explained in the post ...
1
vote
1answer
61 views

Generate random smooth 2D closed curves

I would like to know how can I generate a collection of random 2D closed smooth curves. I thought about generating a random 3D surface with random peaks, and then intersecting the Z=0 plane with it, ...
-1
votes
0answers
45 views

Difference between local and adaptive time stepping

What is the difference between local time stepping and adaptive time stepping in a numerical computation?
0
votes
0answers
13 views

Grid Independence Study

Is the change in time step necessary for the grid independent study? As the CFL is based on the relation between dt and dx. In mesh independent study, only change should be mesh i.e, dx isn't it so?
1
vote
0answers
51 views

1-D Conduction Steady state heat transfer using FD

I have tried to solve 1-D Conduction Steady state heat transfer problems in Matlab (see below). Here is the 1-D model: T''[x] == 0, T[0] == 100, T'[100] == 0 ...
2
votes
1answer
58 views

Mathematical foundations of the fractional step method

The well-known method for solving multi-physics time-evolution problems called "the method of fractional steps" or "the method of splitting" usually applies to PDEs which have a ...
3
votes
3answers
87 views

What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate

What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
0
votes
0answers
18 views

Producing Voronoi diagram in three dimensional

A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D. Although there are many algorithms to construct a Voronoi diagram, some of them are faster ...
0
votes
0answers
17 views

Set of integrators do not consistently solve an equation in Python

I must solve the following second order differential equation: $\delta \phi^{''}_{\mathbf{k}}+(3-\epsilon)\delta \phi^{'}_{\mathbf{k}}+\left(\frac{k^2}{a^2 H^2}+\frac{V_{,\phi\phi}}{H^2}-6\epsilon +4\...
0
votes
0answers
16 views

Calypso with quantum espresso for nanoparticles

Any one uses Calypso structure prediction? http://www.calypso.cn/documentation/ I want to run a two type molecules nanoparticle structure Any suggestions will be helpfull. Or if any other tools for ...
0
votes
1answer
59 views

Extracting data from VTK simulations using C++

I have been given a few numerical simulations regarding fluid mixing and have been asked to extract a few parameters from them using C++. Altogether there are about 1000 VTK files per simulation, and ...
0
votes
0answers
20 views

PETSc configure does not allow mkl_sparse in Cygwin on Windows

I'm trying to use PETSc's AIJMKL sparse matrix in Windows. I'm configuring and building under Cygwin but using it directly in Windows (libpetsc.lib and libpetsc.dll ...
0
votes
1answer
249 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)...
-3
votes
0answers
21 views

dolfin-convert take an error for converting the .msh file with hybrid mesh to .xml file [closed]

when I try to use the dolfin-convert for converting the .msh file obtained by 'gmsh -2 file_name.geo' to the .xml file , I encountered a question as follow: ...
4
votes
1answer
71 views

Imposing no flux boundary conditions on variants of the Cahn-Hilliard equation using Finite Differences in Python

I have been looking into simulations of phase separation in variants of the Cahn-Hilliard system and have been running into issues with implementing no flux boundary conditions on certain variants. ...
3
votes
1answer
134 views

Solving the heat diffusion equation with source term

I am trying to solve the 1-D heat equation numerically with a variable source term. The system is basically a tank containing styrene in which it polymerizes to liberate heat. I have assumed that the ...
1
vote
2answers
177 views

Solve wave equation with discontinuous coefficients numerically?

I would like to solve the following equation $$\frac{\partial^2 y}{\partial t^2} - c^2(x,t)\frac{\partial^2 y}{\partial x^2}=0,$$ for $y=y(x,t)$ numerically. The wave speed, $c(x,t)$, is of the form $$...
1
vote
0answers
61 views

Fortune algorithm for voronoi diagram

Although there are many algorithms to construct Voronoi diagram, some of them are faster than others. Based on my knowledge Fortune algorithm is fastest for construct Voronoi diagram either in two ...
0
votes
2answers
141 views

How GMRES method finds smallest singular value and the corresponding singular vectors of a matrix?

https://stackoverflow.com Krylov solvers for iterative computation of the smallest singular value and the corrensponding singular vectors of a matrix Edit: This is a follow-up question to How to ...
0
votes
0answers
53 views

The error in SOR algorithm suddenly falls to zero when it reaches 1e-7 range

I am solving the Poisson equation for heterojunction using Fortran90. I use the SOR algorithm to arrive at the potential profile. I see the weird behavior where the error (the difference between the $...
2
votes
1answer
64 views

Accelerating convergence of a generalized continued fraction

I wish to compute $$ \frac{1}{1 + \frac{1^3}{1 + \frac{2^3}{1 + \frac{3^3}{1+\cdots} } } } $$ to high accuracy. To start, I tried computing $$ \frac{1}{1 + \frac{1^2}{1 + \frac{2^2}{1 + \frac{3^2}{1+\...
-3
votes
0answers
30 views

implement an optimal control model with python [closed]

Please help me to implement this model of optimal control (python): $$[\hat{T}_{high},\hat{T}_{low}] = \arg \min_{T_{high},T_{low}} J_{constraint}$$ where: $$J_{constraint} = \frac{t_2+t_3+\alpha_1\...
0
votes
1answer
77 views

Is it possible to resample grid in such a way so that continuous objects remain continuous?

Suppose I rasterize a rectangle of width 2.5 gridpoints and get the values as shown: =============== | 0 | 1 | 1 | 0.5 | 0 | Now I resample that ...
-1
votes
0answers
16 views

Share Folder Missing File [closed]

I have two PCs (let's say PC1 and PC2) connected to each other through the LAN cable. From this connection, I created a share folder which can be accessed from both PCs. However, most of the time when ...
3
votes
1answer
104 views

Compute the function between two images

Take an image $f$ with some characters on it (below, hjFu3). Let's apply a filter $h$ on it to obtain a second image $g$ where the text is not visible. Is there a way to compute what kind of filter $...
10
votes
1answer
157 views

Benchmark problems for eigenvalue reordering algorithms sought

Every real matrix $A$ can be reduce to real Schur form $T = U^T A U$ using an orthogonal similiary transform $U$. Here the matrix $T$ is quasi-triangular form with 1 by 1 or 2 by 2 blocks on the main ...
2
votes
0answers
50 views

Determine the anti-derivative of 2D vector field

I have data on a (x,y) grid with scalar values (time) at each point. I have used the numpy gradient function and linear interpolation to determine the gradient vector Velocity (Vx,Vy) at each point (...
8
votes
1answer
365 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
22 views

Choosing appropriate timestep for FDTD and PIC algorithms

I'm doing some particle-in-cell (PIC) simulations of propagation of short pulses in plasmas with a widely used code. This code uses Yee's field solver. So, the timestep must be lower than the Courant ...
1
vote
1answer
231 views

DNS simulation in industry

I have this idea in my mind that Direct Numerical Simulation (DNS) is only used in research since the Reynolds numbers of industrial applications are too high and require computer horsepower we don't ...
1
vote
4answers
1k views

Which C++ Multi-objective Optimization libraries allows the addition of custom problems and custom algorithms?

I'm working on a custom discrete and constrained multi-objective optimization problem and I'd like to know which libraries or platforms that implement algorithms like ...
3
votes
1answer
416 views

what is the best theory/model to use for prediction in multivariate data?

I use software for pollutant propagation on rivers that takes as input a set of parameters ($p_1,p_2,\ldots,p_n$) and creates an output file which is basically a matrix where on each row the ...
0
votes
0answers
25 views

Abnormalities when using SOR to solve the Poisson Equation

I am trying to solve the Poisson equation for Heterostructures using SOR. The equation to solve looks lik I have discretized the Poisson equation using finite difference and my code is written in ...
0
votes
1answer
44 views

How to optimize nuclear norm subject to positive semidefinite constraints?

For finite dimensional symmetric positive semidefinite matrices $A$ and $B$, I would like to solve \begin{align}&\min |X - A|_1 \\ &\text{subject to}\\ &X \preceq B \\ &0 \preceq X\...
2
votes
1answer
68 views

Solving Lotka-Volterra Equations on Python

I'm trying to plot Lotka-Volterra Equations using Python. I am a real beginner when it comes to Python. I have these two equations: $$\frac{dR}{dt}=\alpha R-\gamma RF$$ and $$\frac{dF}{dt}=-\beta F+\...
2
votes
3answers
132 views

Flux sign and face normal confusion in finite volume method

I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
0
votes
1answer
91 views

Is it possible to predict solution oscillation before solving the system by looking at coefficient matrix?

Question When it is about solving a system of equations, is it possible to predict that whether high-frequency noise (e.g. checker-boarding) is likely to appear in the converged solution by looking at ...
2
votes
0answers
162 views

Extracting FEM matrices in matlab pde toolbox

I am trying to follow the dynamic linear elasticity in Matlab, link here. My goal is to extract the FE Matrices using the function assembleFEMatrices in matlab and solve the resulting system of second-...

15 30 50 per page
1
2 3 4 5
179