All Questions

Filter by
Sorted by
Tagged with
1
vote
1answer
161 views

Where can an undergraduate go to find cores on a budget?

I've may have reached a point in my neural network research that I cannot continue without significant financial investment. I am using neuroevolution to evolve a network on the EMNIST data set. It ...
1
vote
0answers
109 views

Numerically compute PDF given a function

Consider $[0,1]$ with the Lebesgue measure $m$ and $f:[0,1]\to \mathbb{R}$, and $x$ a uniformly distributed random variable in $[0,1]$. Then, $f(x)$ itself define a new random variable. We can then ...
1
vote
2answers
352 views

Mass conservation in 1d diffusion by method of lines

I am solving the 1D diffusion equation by discretization using the method of lines. My problem is that I don't manage to ensure mass conservation. I have read many similar questions about the topic ...
1
vote
1answer
125 views

Crank-Nicholson for diffusion-advection vs diffusion equation

Let's consider the following 1D diffusion equation: $\frac{\partial u}{\partial t} = xk \frac{\partial}{\partial x}(\frac{1}{x}\frac{\partial u}{\partial x})$ where we assume that the diffusion ...
1
vote
1answer
57 views

Four-noded rectangular element shape functions

I works on a project where I need to compute a modal analysis of an acoustic cavity. The cavity is rigid which translates the problem to the following equation $$\frac{\partial^2p}{\partial{}x^2}+\...
1
vote
1answer
1k views

Improper Numerical integral

I am self teaching myself python and computational physics via Mark Newmans book Computational Physics the exercise is 5.17 of Computational Physics. I have to shift the limits of integration for an ...
1
vote
1answer
218 views

Use SLEPc from Matlab

Is there a direct way to use SLEPc from Matlab? I remember that in some old manuals there was some Matlab interface. However, in the last one, I cannot find any reference to this. For me, it would be ...
1
vote
0answers
43 views

Comparison of convection time - theoretical value vs computed

This is a follow up to my previous post here, I'm solving for convection in 1D $$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$ The discretization of the above equation is ...
1
vote
1answer
293 views

FFT Poisson Solver for non-uniform grid

I have a 3D solver for the incompressible Navier-Stokes equations which uses a FFT library for the Poisson equation with a uniform grid on all directions. In 2D the Poisson equation is given by: $$ ...
1
vote
1answer
208 views

Converge rate analysis: issue with time convergence

I have written a code which solves the incompressible formulation of the Navier-Stokes equations. It uses high-order methods both for time and spatial derivatives. I have been conducting convergence ...
1
vote
2answers
113 views

Solving a parameter estimation problem using trajectory optimization

This is a follow-up to my previous question here I've the following system of equations for studying information flow in the below graph, $$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise ...
1
vote
1answer
431 views

Feasibility checking

Consider the following optimization problem: $Min\;\;\; CX$ $AX\geq b$ $x_ix_j= x_s x_t\;\;\; i\neq j \neq s\neq t$ $x_j\geq 0;$ Where $A$ is the adjacency matrix and $C$ is a constant vector. ...
1
vote
0answers
44 views

When numerically computing eigenstates during a coupled-mode-space NEGF calculation, do phases matter?

The coupled mode space NEGF method for computing transistor characteristics involves expanding the electronic wavefunction in a mode space basis $$\Psi(x,y,z) = \sum_n\phi_n(x)\xi_n(y,z;x)$$ where $\...
1
vote
3answers
1k views

Algorithm to compute the intersection of two lines given their cartesian equations

I'm looking for a way to compute the coordinates of the intersection of two lines. Each lines are defined with a point and a normal vector. We can assume than the normal vectors are not zero and ...
1
vote
1answer
1k views

Convex Polygon Intersection

Determining the intersection of two convex polygons is one of the fundamental problems in computational geometry . I'm asking for an algorithm having: INPUT: Given two convex polygons P and Q in 2D (...
1
vote
1answer
142 views

FEM oscillations for polynomials of degree 1

I have the following eliptic 1-D problem $$-\mu u'' + \beta u' = 1$$ $$u(0) = u'(1) = 1$$ where $\mu = 10e^{-5}$ and $\beta = 1$. For this specific problem I am using the following space steps $h=[0.1,...
1
vote
1answer
56 views

Is there an upper bound for fill-ins for indefinite triangular factorization?

For $A=LU$, or $A=LDL^T$ factorization, bandwidth is preserved when there is no pivoting. This is true even for indefinite A, see question. However, when there is pivoting band structure is destroyed, ...
1
vote
3answers
188 views

How to choose $h$ in SPH?

I have a 2D implementation of smoothed particle hydrodynamics up and running, however when I tried to move it to 3D, using the appropriate 3D kernels, particles always tend to go apart from each other....
1
vote
1answer
84 views

Invert a matrix only on a subset of variables / Compute the “equivalent circuit”

Suppose I have a complicatedly shaped conductor with inhomogeneous conductivity. The conductor is modeled using the Finite Element Method. The conductor has electrical contacts on both ends. Those ...
1
vote
1answer
115 views

Non-Linear advection diffusion with nondifferetiable advection term

I'm looking at Murray's book: Mathematical biology: an introduction , first volume, pag. 404 In particular, I'm interested to solve the following PDE: $$\partial_t u = \partial_x (\text{sign}(x) u) + \...
1
vote
3answers
346 views

rank-deficient NNLS

I want to find the minimum-norm solution to a rank-deficient least-squares problem, subject to positivity constraints, e.g. $$\min_x\ \|x\|^2 \quad s.t.\quad Ax = b,\ x \geq 0$$ where $A$ is large, ...
1
vote
1answer
581 views

Crank-Nicolson method for inhomogeneous advection equation

Suppose we have the inhomogeneous advection equation $$\left(\frac{\partial}{\partial x}+\frac{1}{c}\frac{\partial}{\partial t}\right)u(t,x)=v(t,x)$$ for $u,v:\mathbb{R}\times\mathbb{R}\to\mathbb{R}$ (...
1
vote
3answers
197 views

Optimization of a blackbox function

Let's say that we have an objective function $f(\mathbf x,\mathbf y)$ which has the parameters $\mathbf x=[x_1\ldots x_n]$ and $\mathbf y=[y_1\ldots y_n]$. Here, $\mathbf y$ is a blackbox variable ...
1
vote
1answer
772 views

Direct multiple shooting (numerical optimal control)

Please, I am currently implementing direct multiple shooting methods* and I need one simple but fundamental concept answered: When I want to provide not only objective function value (the result of ...
1
vote
2answers
3k views

scipy.integrate.odeint: how can odeint access a parameter set that is evolving independently of it?

I might have some non-linear ODEs that are being solved by scipy.integrate.odeint. However, a parameter at each time step might have to be updated by using a non-DE ...
1
vote
2answers
82 views

Maintain Uniform Distribution across Subranges

Note: this is a continuation of Generate Random Number outside Bounds. I have a function (thanks to the previous question) with the following prototype which returns an integer in the range $[0,b]$, $...
1
vote
2answers
460 views

What method do you suggest to solve this minimax, quadratic in both variables problem?

I have a problem of the form, \begin{align} minimize_{y} maximize_{x}&\quad x^T y - y^T (B\odot x x^T) y\\ s.t. &x\in [l,u]\\ &Ay=b \end{align} How to efficiently solve this problem? ...
1
vote
1answer
127 views

TDMA with 3rd order upwind scheme

I'm trying to implement a model I found in a paper, but there is something I do not understand. The authors say they use TDMA to solve their equations; however, they use a 3rd order upwind biased ...
1
vote
2answers
314 views

Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong

I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
1
vote
1answer
324 views

Solving first versus second order PDE

I am trying to numerically solve a PDE, and just had a question as to the validity of a certain approach. For example, given the PDE: $$ \frac {\partial ^2 E}{\partial t^2} = - k\frac {\partial E}{\...
1
vote
1answer
112 views

How to do Weierstrass-transform in MATLAB?

I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform) on them. So I have the wave functions ($\Psi$), and the continuous ...
1
vote
0answers
526 views

Looking for C++ function for performing optimization of parameters for multivariable function

I am adapting a Java program from C++ and need a C++ function to perform the same task as the Java BOBYQAOptimizer() function. Can anyone recommend a C/C++ library with equivalent or similar functions ...
1
vote
0answers
66 views

Determine Lagrange nodal variables of a simplex $T$

Consider a simplex $T$ in $R^d$ with $N_1(T) = \left\{N_i\right\}_{i=0}^{d}\subset P_1^{*}(T)$ be the Lagrange nodal variables (or nodal evaluation). By the Riesz representation theorem, there exist ...
1
vote
0answers
185 views

Numerically solving a system of stiff nonlinear PDEs

I am attempting to numerically solve the following: \begin{align} \frac {\partial y_1}{\partial t} &= i(y_2y_3 - y_2^*y_3^*) - y_1 \tag{1}\\ \frac {\partial y_2}{\partial t} &= y_1^*y_3 - y_2 ...
1
vote
2answers
226 views

Effective way to build the neighbor's list in MD

I'm trying to implement the following form of the cell/neighbor list method in my MD code. I have divided my simulation box into a fixed number of cells, and according to its positions, I have ...
1
vote
1answer
439 views

Gnuplot: How can I determine the maxima of a fit function in gnuplot?

I have a set of data data.txt which can be fit to a Gaussian function, f(x). I want to determine the coordinates of the point of ...
1
vote
1answer
93 views

Classification of method for solving PDEs

If I have a system of equations as follows (where $i = \sqrt{-1}$): $$ \frac {\partial A}{\partial t} = iA^*B - A \tag{1} \\ $$ $$ \frac {\partial B}{\partial z} = AB^* - B \tag{2} $$ Using the ...
1
vote
1answer
131 views

How to compute turbulent energy cascade

I need to compute the kinetic energy cascade using a finite volume solution in an equally spaced grid. I wonder if it is more correct to first compute the kinetic energy in the space (or time) domain, ...
1
vote
0answers
828 views

linearly interpolate and determine gradients for data on non-uniform grid

I have measurements of a quantity on a 3d grid. My measurements are distributed on four x-y planes similar to what is shown in the image below. The measurements roughly follow a Cartesian grid but ...
1
vote
0answers
76 views

PDE discretization (via finite difference sheme) question

So after posting this question and reading all your comments I would like to make this new question (update). If you consider the three equations presented here: $$\frac{\partial \rho}{\partial t} +\...
1
vote
0answers
1k views

Crank-Nicolson for 2nd- and 4th-order finite differences

I modeled the heat equation, $$ u_t = au_{xx} $$ using the common 2nd-order Crank-Nicolson scheme, $$ \frac{u^{n+1}_i-u^{n}_i}{dt} = \frac{a}{2\,dx}\left(u_{i-1}^{n+1}+u_{i+1}^{n+1}-2u_i^{n+1} + u_{i-...
1
vote
0answers
143 views

Using backward difference approximations for higher order derivatives

I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of ...
1
vote
1answer
80 views

Isotropic thermal expansion

I frequently see the equation $$ \sigma_t = E\alpha \Delta T $$ as the equation for thermal stress. Where $E$ is Young's modulus, $\alpha$ is the CTE, and $\Delta T$ is the change in temperature. ...
0
votes
0answers
33 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 $A$. $$\...
0
votes
1answer
220 views

Is there any rapid way to calculate the determinant of NXN covariance matrix?

I searched the web and found some C code for calculating the determinant of a $n\times n$ matrix. This code however seems timing complexity, and run pretty slow especially when handling a larger ...
0
votes
1answer
721 views

roots of polynomials of high degree: LinAlgError: Eigenvalues did not converge

I wrote a simple script to generate random polynoimals $\displaystyle f(z)= \sum_{k=0}^N a_k \frac{z^k}{\sqrt{k!}} $ of high degree and find their roots. For more discussion on random polyomials see ...
0
votes
2answers
351 views

Numerical evaluation of the first and second complete elliptic integrals

To get a numerical evaluation of the first (K) and second (E) complete elliptic integrals: $$K(k)=\int_0^1\frac{dt}{(1-t^2)^{1/2}(1-k^2t^2)^{1/2}}, \ \ \ \ \ E(k)=\int_0^1\frac{(1-k^2t^2)^{1/2}}{(1-t^...
0
votes
1answer
64 views

openmp critical

Following this question, for the code below (from MS OpenMP docs example) ...
0
votes
2answers
675 views

Mixed formulation of the Poisson equation (FEM)

I'm solving the Dirichlet problem for the Poisson equation in a 2d domain $D$: $$ \begin{cases} \Delta u = 0 \quad \text{in $D$}, \\ u|_{\partial D} = u_0. \end{cases} $$ I'm interested in ...
0
votes
2answers
312 views

Calculating integrals for a function approximated by Chebyshev polynomials

Setup (complete, but all very standard): My problem is how to best calculate the cumulative integral of a function which comes out of Spectral Collocation with a chebyshev basis. Take some function $...

15 30 50 per page