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64 views

How to implement the following Finite Element method for Burgers' equation?

I am trying to replicate this result. It involves using the Galerkin finite element approach onto the viscous Burgers' equation. However, my implementation (in R) seems to be giving me wrong results....
7
votes
1answer
200 views

Do computational scientists typically also become domain experts?

Let's say I'm interested in fluid dynamics, specifically in fluid-structure interactions -- and I want to get into modeling, simulations and experiments. I am a mathematics student by training, ...
2
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0answers
35 views

Equivalent of multiple-scale analysis for a linear ODE

I came across the method of multiple-scale analysis and was intrigued, because I am trying to solve a linear ODE with multiple characteristic timescales. When I apply the method as described, say, ...
3
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0answers
31 views

Sparsity-Promoting Convex Optimization Over Simplex

Say we want to find a sparse approximate minimizer to the function $f(x) : \mathbb{R}^d \to \mathbb{R}$. Then in line with the work in the field of compressed sensing, we can instead minimize $$f(x) + ...
2
votes
1answer
34 views

Can I solve a model in GEKKO with Black Box, Simulated Annealing or GA solvers?

I'm trying to use my current GEKKO model with different solvers methodologies. I don't know if I can also use global optimisation solvers as GA, Simulated Annealing o Differential Evolution. I need ...
1
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1answer
54 views

What is the exponential trick to include laplacian term in Rayleigh-Bernard simulation

I have come across a Rayleigh-Bernard simulation code which doesn't have the laplacian term but an integrating factor (in the exponential form) containing viscosity and diffusivity. I found out that ...
0
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0answers
32 views

Grids for atmosphere simulation with finite volumes on the globe

I am currently in the early construction process of building a simple CFD model of a rotating planetary atmosphere. The planet should be allowed to tilt significantly, so that a time-dependent source ...
3
votes
1answer
79 views

Calculating the Convolution Using DFT (FFT)

I have the following convolution as part of a numerical simulation. $$T(r)=\int \mathrm{d}^3r_2\, p(r_2)f(r_2)\alpha(r-r_2)\, .$$ My problem is that the analytical expressions for $f$ and $p$ do ...
0
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0answers
63 views

How one can simulate a system given by differential equation?

I want to simulate a diffusion environment given by the differential equation $$\frac{\partial u(x,y,t)}{\partial t}=D\left(\frac{\partial^2 u(x,y,t)}{\partial x^2}+\frac{\partial^2 u(x,y,t)}{\...
0
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1answer
121 views

Prescribing variables as an excitation in Runge-Kutta method

I am using Runge-Kutta to solve a $3 \times 3$ 2nd order linear ODE $$M x'' + C x' + K x = 0$$ and initial conditions are all zeros. Then I prescribe the 2nd variable to follow a given path. As for ...
1
vote
1answer
44 views

Incomplete LU decomposition of sparse matrix

I have a sparse matrix stored in CSR format. For this matrix, I would like to get the incomplete LU decomposition. I tried to find algorithms which can utilize the CSR format but I could not find ...
4
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0answers
29 views

Implementation of Lanczos method that returns tridiagonal matrix

The Lanczos method can be used to obtain extremal eigenpairs of sparse symmetric or hermitian matrices. I know there are several implementations of the Lanczos method (as well as Arnoldi, Davidson, ...
4
votes
1answer
38 views

Binary combinatorial optimization with hard to compute costs

I have a combinatorial problem regarding the optimal placement of sensors. I want to find the optimal placement of $N$ sensors, given $M$ possible locations, $N < M$. Right now I'm working with ...
0
votes
1answer
504 views

Power series regression linear fit in VBA excel

I wrote a program that calculates the best fit in VBA excel for the following model $$ y_k=c_1x_k+c_0+c_{-1}(x_k)^{-1} $$ solving for the best fit parameters $c_1$, $c_0$, and $c_{-1}$. However I ...
0
votes
1answer
24 views

Change of random variables and check by plot

Question As a test, I transform a uniform distribution over the unit square. But when I check the transformed distribution with Monte Carlo, it is wrong. What went wrong? Thanks. Problem Random ...
0
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0answers
35 views

Least square approximation of a polynomial with a constraint on the derivative in Python

I'm trying to fit a polynomial of the third degree through a number of points. This could be a very simple problem when not constraining the derivative. I found some promising solutions using CVXPY to ...
0
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1answer
68 views

Numerov method for Schrodinger equation

While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method. I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. ...
0
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1answer
54 views

Determination of Young's Modulus for a Finite Element Code

I am writing a finite element code for my final year project of BS Mechanical Engineering. The geometry is an integration of several parts composed of different materials. I don't have exact values of ...
0
votes
1answer
84 views

Well-posedness of Navier-Stokes equation

Before running a simulation for turbulence (e.g Rayleigh-Benard Convection), how do we check for well-posedness of Navier-Stokes with other equations for a given boundary condition?? Can someone ...
5
votes
1answer
471 views

Finite volume a posteriori error estimation

I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated ...
25
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6answers
4k views

How can the gravitational n-body problem be solved in parallel?

How can the gravitational n-body problem be solved numerically in parallel? Is precision-complexity tradeoff possible? How does precision influence the quality of the model?
1
vote
1answer
2k views

2D cross section from 3D surface

I am trying to apply the "restoring force surface" method to a dynamic linear system. The idea behind this method is that, knowing acceleration, displacement, velocity and input force it is possible ...
2
votes
1answer
61 views

Plasma Simulation Software Advice?

I’m looking for software that can simulate “hot” plasmas of multiple ion species...so some sort of simulation software that could calculate ion temperature and density distributions taking into ...
5
votes
1answer
233 views

Shape measure for C-shaped objects

There are many well defined measures for many basic geometrical objects such as rectangularity (area coverage of minimum bounding rectangle), triangularity (area coverage of minimum enclosing triangle)...
6
votes
1answer
94 views

Optimization algorithm / approach for suggesting what goods to buy and sell in a marketplace?

A toy problem would probably be best to explain it this. Let's say we have 100 people, each with 4 unique types of items (to simplify things, let's say it's the same four types of items for each ...
1
vote
1answer
343 views

Difficult bug in my 2D Compressible Euler solver

For the past few days, I have been writing a numerical solver for the 2D compressible Euler equations for an ideal gas. My numerical method has been the Local Lax Friedrichs or "Rusanov's method." ...
3
votes
1answer
119 views

Single nodes after mpmetis partitioning

I was checking partitioning capabilities of Metis (mpmetis) when I noticed, that it leaves two single nodes. I have marked them in red Have you seen something similar or maybe it is my mistake? The ...
3
votes
1answer
336 views

Limitations with dynamical systems vs. PDEs?

As a computational scientist, are there limitations to studying dynamical systems — systems of odes in which each state variable evolves with time — compared to studying PDEs? For instance, it seems ...
1
vote
0answers
901 views

Pixel-To-Angle Transformation in Camera Image

I'm trying to localize points I see in a camera image in terms of azimuth and elevation and match points between shots. Individual shots should differ only in rotation around the camera's center (...
2
votes
1answer
124 views

Why don't we call the simulation “a model for …”?

When a set of model equations, e.g. some coupled differential equations, has solutions that behave in ways similar to real-life phenomena such as blood flow in the heart, a wave movement, or a plate ...
24
votes
8answers
4k views

What software is good to use for parallel debugging?

I'm not running any parallel code right now, but I anticipate running parallel code in the future using a hybrid of OpenMP and MPI. Debuggers have been invaluable tools for me when running serial ...
1
vote
1answer
47 views

How to use QZ decomposition for single matrix in Matlab?

Can I use QZ decomposition on a single square matrix in Matlab? Like, [Aa,Q,Z]=qz(A);
0
votes
1answer
41 views

How to define $P0-$ Piecewise constant basis function in finite element method?

Suppose if we take $X_h(G)$ as finite element space then this space (space of piecewise constant basis function)is defined as $$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$ where $\mathbb{T}$ is a ...
5
votes
0answers
78 views

Sensitivity of BFGS to the accuracy of the gradient

I am studying how to speed-up the BFGS method using quantum computing techniques. I have used a method of speeding up the gradient of the function, but it sacrifices the precision value of the ...
2
votes
1answer
59 views

Activation function with special conditions in machine learning

I only have a basic understanding of deep learning, but looking through it I had an idea on how to approximate global minima of the NN. However, for it's activation function I am only able to use: ...
1
vote
1answer
59 views

Classical vs. modified Gram-Schmidt

It is often said that modified Gram-Schmidt is more robust with respect to rounding errors than classical Gram-Schmidt, but it is very hard to find a good explanation / example of why this is so. Can ...
10
votes
1answer
346 views

DG local equation, how to interpret mean-averaged test function

In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following ...
3
votes
1answer
369 views

What's the terminology for this alternative minimization algorithm?

Say the model is $F(x_1)G(x_2)Z(x_3) = y \in \mathbb{R}^N$, with $F,G,Z$ explicitly known, we are given observation of $y$ as $y_b \in \mathbb{R}^N$ to find the value of $x_1$, $x_2$, $x_3$ for each ...
2
votes
2answers
78 views

How to include penalty in a Objective Function with Python? GEKKO

I'm trying to include a "great M" penalty in my objective function. I want use the entry x vector values as entry values in a function. A fixed maximum value is took initially for the returned value ...
0
votes
0answers
40 views

Cubature rule in unit Sphere in $\mathbb{R}^{3}$

I need to find the cubature rule for the following integration $$\int_{S^{2}} f(s,\tilde{s})d\tilde{s} ds,$$ where $S^2$ is the unit sphere in $\mathbb{R}^{3}$.
1
vote
1answer
51 views

Finding curves where function goes to zero in two dimensions

Suppose $f(x,y)$ is a complex function of two real arguments with roots* that are not discrete points but lie in curves. (Is there are term for this characteristic?) An example is shown below: the ...
1
vote
0answers
12 views

Error on the fit parameters when several good fits exist

I am using the reduced chi-squared statistic to determine the goodness of fit. I run several simulations and determine that a parameter 'p' has a certain range of values that all give values between 0....
1
vote
1answer
62 views

Best way of storing numerical data in a compact manner, while leaving it accessible for tools like GnuPlot?

My simulation, written in C++, generates a large amount (roughly ~500) of text files for each set of parameters I try to simulate, with four columns of ~5k double values in each file. Furthermore, to ...
3
votes
2answers
89 views

MINLP with GEKKO - Modeling discrete variables

I'm trying to define a MINLP optimization problem with GEKKO in Python, and I want to use some variables with fixed values. For my first variable, x1, I need to define the following values (as would ...
1
vote
2answers
673 views

2D Ising Model, heat capacity decreases with lattice size

The problem I'm trying to make a metropolis simulation of the 2D Ising model. Basically, it's the following, for each monte-carlo step: Visit each lattice site, Compute energy required to flip ...
0
votes
1answer
60 views

ISING2D with Mathematica. Searching a correct way to compute the heat capacity (mean values over several iterations)

I'm trying compute the heat capacity $C_v$ out of my simulation for the 2D-Ising model which is given by $C_v = \frac{\langle E^2 \rangle - \langle E \rangle^2}{T^2N^2}$ ($E$: Energy, $T$: ...
1
vote
0answers
24 views

Fast convergence of smoothing of periodic noise

I have essentially periodic data from a simulation (not exactly periodic but is qualitatively fairly periodic), and I'd like to take an average or noise filter of some sort that I can get a well ...
6
votes
1answer
281 views

Iterative linear solver for “ugly” saddle point system

I am a graduate student majoring scientific computing. The numeric model I made caused a very ugly-looking saddle-point linear system. It is not symmetric at all and I will attach the sparsity pattern ...
0
votes
1answer
74 views

Software to simulate molten salt flow and thermodynamic operations

I was curious if there was any software (preferably in C++, Java, and/or python) that could be used to simulate the following: Heat capacity of a fluid Heat transfer through a liquid and a solid ...
0
votes
1answer
93 views

How to set an initial guess for the iterative solver in Comsol?

How to set the initial guess for the iterative solver GMRES or FGMRES for linear problems (Helmholtz equation of RF module) in Comsol?

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