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183 views

Iterative algorithm prove precise conditions for convergence

Question: Consider the iterative improvement algorithm below. Starting with $Az_i = r_i$ and $(A + E)\hat{z}_i = r_i$ derive a formula showing how the absolute error in the $(i + 1)^{st}$ iterate $\...
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198 views

Histogram separation energy equation based on Bhattacharyya

I am working in level set method, specially Lankton method paper. I try to implement Histogram Separation (HS) Energy problem (Part III.C). It based on Bhattacharyya to control the evolution of ...
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0answers
2k views

Finite differences and Neumann boundary conditions

I am dealing with a highly nonlinear system of two PDEs. I already have a code to solve the system in case of Dirichlet boundary conditions. The explicit system is: $$ \begin{eqnarray*} \partial_{t}u ...
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0answers
68 views

Tecplot Span-Wise Loading Visualization

all. I have data from a CFD simulation for a wing, and I need to obtain a visualization of the span-wise load distribution. I'm attempting to do this using Tecplot. I've tried using 'slices' and '...
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0answers
216 views

advection diffusion equation

Would you know what is the condition for stability for the advection-diffusion equation where we treat the diffusion part using Crank-Nicholson and the advection part using FCTS (forward in time ...
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0answers
194 views

Givens method for sparse matrix

I have a (very) large sparse matrix in CSC form and I'm supposed to factorize it. I've read that between Givens and Householder transformations, Givens is better for a sparse matrix. The problem is ...
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132 views

Algorithms to compute largest gap between smallest nonzero eigenvalues of sparse symmetric matrix

I am looking mainly for c/c++ implementations but also for theoretical algorithms to compute gaps between smallest positive eigenvalues of symmetric, singular matrix or real numbers. To be precise, I ...
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0answers
692 views

how to visualize velocity from Lagrangian particle tracking method

I have few particle's position and velocity information as a function of time. Particle is following a trajectory path, while doing so, one particle may disappear, other particle may appear. Particle ...
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0answers
85 views

References on the topic of DEM and XDEM

DEM: discrete element method. XDEM: extended discrete element method. For my current project of furnace simulation with granular materials, I am interested in the methods mentioned above. I have not ...
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0answers
57 views

Energy anomolies in many body simulation

I am trying to simulate the gravitational interaction between many bodies. I am using a direct PP force calculation and a 4th order symplectic integrator with a variable step size. The energy of ...
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0answers
3k views

Stationary solution converge but time dependent doesn't

I've coupled a COMSOL model for fluid dynamics with a very simple pde that model the transport of humidity in air. When I solve it for the stationary case, the solution converge easily, but when I ...
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226 views

computation complexity of OLS in estimating a VAR model

Could someone tell me the computation cost of using Ordinary least squares in estimating a Vector autoregression model? I am thinking the cost is O(n) where n is the number of the training instance. ...
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420 views

How to move particles in a variational Monte Carlo simulation?

I'm attempting to implement some code that moves particles and then calculated the acceptance/rejection of the move, but I'm stuck in a rut. Here is my Python code: ...
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0answers
166 views

Permissive Math Library for Parameter Statistics in C++

I am looking for recommendations for a C++ math library, with a permissive licence, well suited to calculating a wide variety of statistics on segmentations of timebased parameter data. I would be ...
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1answer
1k views

Faster code for double integration using Gauss-Legendre quadrature

I came with a the following code to evaluate a double integral using Gauss Legendre quadrature in MatLab ...
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1answer
34 views

Generating pseudorandom sequences based on measured sequences

I'm looking for an algorithm to generate discrete-time pseudorandom sequences based on other sequences I already have that would be used to train the algorithm. More specifically, I have some time-...
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1answer
310 views

Applying Runge-Kutta to nonlinear system of PDEs

I am applying a 4th order Runge-Kutta code, using the method of lines, to solve the following: \begin{equation} \frac {\partial y_1}{\partial t} = y_2 y_3 - C_1 y_1 \end{equation} \begin{equation} \...
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1answer
236 views

Robust Counterpart of an uncertain LP

Consider the following robust optimization problem: min c'x s.t.: $Ax\geq b \;\;\forall (A,b)\in \mathcal{U}$. Why can the robust counterpart of the problem be written in this form? $min_x{\{ ...
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0answers
28 views

Calculating surface integral on Cartesian grid

I am trying to calculate surface integral for the following problem (see figure). I have the vertex coordinates $x,y,z$ as well as face center coordinates $x_m,y_m,z_m$. If I have all the interpolated ...
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0answers
46 views

Which programming language is using for the GUI of Star-CCM+?

I am not sure if this is the suitable platform to post this question, so apologies if it's not. I am wondering which programming language was used in developing the GUI for the simulations software ...
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0answers
14 views

how to compute the computational complexity of cellular neural networks?

Anyone, please help us that how to compute the computational complexity of the dynamic state of the single-cell and total cells for the 2D-CNN (two-dimensional cellular neural network). 2D-CNN of M * ...
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0answers
23 views

Could anyone illustrate using examples, the difference between machine epsilon and an underflow?

I have recently gotten started on Numerical Analysis and I was hoping that someone could help clarify the idea of these two concepts to me. Using specific examples of floating-point operations that ...
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2answers
73 views

Is the sine function periodic in $x$ or $y$?

I know sine is $2\pi$-periodic, but some people say the motion is "periodic in..." Would it be periodic in $y$? If we move along the $x$-axis, the function values $y = \sin(x)$ will repeat, ...
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1answer
28 views

An almost surly fine-time game of coin toss where you win with probability $p$

Given a fair coin and a number $p\in(0,1)$. How do you design a game that finishes in a finite number of tosses with a probability of $1$? And further, with the probability $p$ you win the game. I ...
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1answer
49 views

Find mass matrix in a system of linear equations

Given $z_t=\sum_{i=1}^t \theta_iz_{t-i}+v_t $, where $t=1,...,N$ where $N=1024$. I need to write this in matrix form (a system of linear equations) as $\mathsf{A}\mathsf{z} = \mathsf{z} - \mathsf{v}$. ...
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1answer
33 views

surface: rows (Z) must be the same as length (Y) and columns (Z) must be the same as length (X) in octave

I am having a dataset and trying to plot a 3-d plot between the independent and dependent variables.but, I am getting this error whenever I am trying to plot here is my code: ...
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1answer
63 views

How to solve system of equations with almost-zero determinant?

I have a system of equations that I am trying to solve. In matrix form, it's written as $$x(I - S) = b.$$ I am solving for $x$, where $I$ is the identity matrix and $S$ is a matrix where each column ...
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1answer
56 views

How to get free energy surface of a 3d Ising Spin system using Monte Carlo simulation?

I am doing a Monte Carlo Simulation of the properties of a 3D Ising Spin system. I want to get the free energy surface of the spin system from the simulation. It is a magnetization vs free energy ...
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1answer
35 views

FORM by NIKHEF: unexpected behavior wrt summation

I have two almost identical FORM (by NIKHEF) scripts here: script_1 script_2 which differ only in summation at the end. In first case the summation in done in one step, in the second case ...
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1answer
45 views

Integrate using Composite Simpson's rule

In a question, we have been given the speed of a car at time t= 0,2,4,6,.......,20 minutes.But it asks us to approximate the distance travelled by the car in 30 minutes using Composite Simpson's rule. ...
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1answer
183 views

Recursive Algorithm to Calculate Determinant via Expansion of Minors in C#

I have been recently trying to attempt to write an algorithm in C# that would calculate the determinant of a matrix via recursion using the expansion of minors method. I understand that there are ...
-1
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1answer
54 views

Smoothed Particle Hydrodynamics: Weird clustering of particles. Is that normal?

I implemented a rather simple SPH simulation using a cubic-spline-kernel and a simple non-iterative pressure solver as described in this PDF in equation 9. I followed algorithm 1 of that paper (...
-1
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1answer
284 views

Imposing periodic boundary condition for linear advection equation - Node problem

I've spent the whole day trying to figure out what is the correct way to impose (and implement) periodic boundary conditions $u(0,t)=u(1,t)$ for all $t>0$ for the simple advection equation $u_t + v ...
-1
votes
1answer
57 views

Simulating magnetic particles in a field free point generated by two opposing magnets

This is probably a long shot with such a short time, but I've been trying to get theoretical data for a project I'm working on. The project involves using a very simplified version of magnetic ...
-1
votes
1answer
279 views

Finite Element - Flux Calculation

I am solving an advection-diffusion equation using the FEM and am having trouble calculating my fluxes. I start with the equation, $$\frac{\partial n}{\partial t} = \frac{\partial j_{n}}{\partial x}\...
-1
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1answer
112 views

Finite element convergence rate and possion's ratio

I am running simulations of a cantilever beam where it is fixed on one end and negative force applied to the other end. The first simulation is with 4-node linear quadrilateral elements and the other ...
-1
votes
1answer
25 views

Semi-Definite relaxation of non-linear constraint?

I am implementing an optimization problem using semi-definite approach. One of my constraints is of following form $ trace(A∗X)−(k∗trace(A∗X))+(k∗\sqrt {(trace(B∗X)} )==0$ where k is a constant, A ...
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votes
1answer
265 views

Gauss-Seidel method convergence

I am currently programming a code to find the equilibrium function that satisfies the poisson equation in 2D. In order to do this I use finite difference methods and the discrete equation I want to ...
-1
votes
1answer
746 views

Eulerian vs Lagrangian vs Mesh-based vs Meshfree/Meshless methods

Hailing from the scicomp community recently getting into computer-graphics, I have noticed that the scicomp communities talk about mesh-based methods like FDM, FVM, FEM, etc, vs meshfree or meshless ...
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1answer
161 views

ODE15s: unable to meet integration tolerances

I have to solve $$\left\{\begin{matrix} \ddot{R}=-\frac{3}{2}\frac{\dot{R}^{2}}{R}+\frac{1}{R\rho}\left [P_{v}(T_{\infty})-P_{0}-a_{1}t^{2}-a_{2}t+\frac{(L\rho_{g})^{2}}{hT_{\infty}}\dot{R}-4\mu \frac{...
-1
votes
1answer
602 views

Dirichlet boundary condition

I am trying to solve ODEs in matlab using ode15s. Instead of specifying ODEs in the format M * dC/dt = f(C,t) where C is a function of x and t. I want ...
-1
votes
1answer
108 views

solving a non-linear equation with integrals involved

I would like to solve the following equation, wrt $n(e)$ $$f(n(e))=g(n(e)) + \int_{\alpha}^{e} w(n(x))dx $$ The integral there it confuses me. Any suggestion on how I can implement this on a the ...
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1answer
839 views

Any note on Immersed boundary finite difference method?

For parts of a talk, I need a note on "Immersed boundary finite difference method", mainly about the reason of appearing this branch in the finite difference methods, considering mathematical ...
-2
votes
1answer
94 views

Writing a Matlab function after calling the ode45 solver

After using ode45 to solve a set of ODEs, I want to write a Matlab function to take the initial conditions x_0 as inputs and gives the final state x_1 at time T as ...
-2
votes
1answer
56 views

Calculate accuracy order/rate

I was doing error analysis of numerical scheme and I get $L_1$ error for each grid size with $N$ element. I was searching reference to compute accuracy order/rate from that error data but doesn't find ...
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1answer
793 views

openFoam - How to create an intermediate scalar variable and output it?

For learning purposes, how do I create an scalar variable like temperature divided by 2 and outputs it on files generated?
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1answer
275 views

How to solve this differential equation using RK4 in C++?

I have been given the following homework question to solve: I am having trouble writing a RK4 solver in C++ for this ODE. I am also not sure how to plot my solution. Here is my code so far: ...
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votes
1answer
346 views

Solving electron density function for Hydrogen and drawing in 3D

I recently stumbled upon interesting site that has interactive 3D representation of radial electron distribution (atomic orbital). here is the url: http://winter.group.shef.ac.uk/orbitron/AOs/1s/e-...

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