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3
votes
1answer
128 views

calculation of the right hand side of DG FEM (with code)

I got stuck with Hestaven/Warburton's dG-FEM Matlab code. Starting with the file AdvecRHS1D.m, we see in line 11 ...
0
votes
0answers
47 views

Null space for smoothed aggregation algebraic multigrid

I do not really get the point of null space usage for creating the prolongation operator for smoothed aggregation algebraic multigrid. I know what the null space is per definition and I know that the ...
1
vote
1answer
30 views

Draw contour line to represent multiple contours

I have 5 data sets, each includes multiple scatter points. If I use the geom_path function in R, I could obtain 5 contours like the following graph shows. Those five contours are annotated outlines ...
0
votes
1answer
30 views

How to implement the Impulse Based Dynamics for the rigid body dynamics simulation?

I am having hard time learning the method of impulse based dynamics developed by Mirtich for rigid body dynamics simulation. Please help me out if any body has any example code(algorithm) of it. ...
2
votes
1answer
89 views

Differentiation Matrix In DG-FEM - Hesthaven/Warburton

In the book of Hesthaven and Warburton on discontinual Galerkin methods the authors give motivation to the differentiation matrix (page 52), referred to as $D_r(i,j)=\frac{dl_j}{dr}|_{r_i}$ where $l_i(...
2
votes
1answer
61 views

Langevin equation in 4th order Runge-Kutta

I'm trying to figure out how to translate a piece of code from Velocity Verlet to Runge-Kutta, while treating the time step dependence of the thermal noise correctly. The Langevin equation for my ...
3
votes
2answers
98 views

How to reconstruct a 2D field from its integral?

General question I work on the plane where I have a two-dimensional shape $V$ that is cut in a collection of parts $\{V_i\}$ that do not overlap $ V_i ~~\text{s.t.}~~ \bigcup_i \overline{V}_i = \...
2
votes
0answers
14 views

Why I am not able to generate Levy distribution using inverse transform method on MATLAB?

I am trying to generate random numbers using Levy distribution in MATLAB. I am using the inverse transform method to generate random numbers and then plot its histogram for pdf estimation. Then I ...
2
votes
0answers
66 views

Regularized least squares with QR factorization

Consider the regularized least squares problem $$ \min_x || b - A x ||^2 + \lambda^2 ||x||^2 $$ which is equivalent to $$ \min_x \left|\left| \pmatrix{b \\ 0} - \pmatrix{A \\ \lambda I} x \right|\...
2
votes
0answers
37 views

Isosurface extraction when you know the derivatives

I have a complicated equation that defines a shape in 3D, and I would like to generate a surface mesh. The shape is defined by an isosurface, i.e. the function is positive inside the shape and ...
4
votes
0answers
64 views

Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
1
vote
0answers
27 views

turbulant flow modeling [closed]

I have been trying to model the flow in a very thin channel using COMSOL Multyphysics. The laminar flow module does not converge no matter how I change the meshes, or use ramping loads and such. The k-...
1
vote
0answers
29 views

Duplicate Surface Meshes in different Gmsh files

My objective is to get a conformal surface mesh between two geometries meshed independently in different files. By example, I can start with a simple cube in one .geo file and mesh this geometry. ...
1
vote
1answer
28 views

How is the D value being updated at simple RRT algorithm?

I am studying the following lecture (image) regarding 5 iterations of the simple RRT algorithm. I am trying to understand how each value is being updated regarding each iteration. I have figured out ...
1
vote
1answer
56 views

How to get started with numerically solving a Stochastic Navier Stokes equation

I originally posted the question on the math stackexchange, and was told I should try here. I’m researching Stochastic PDE, in particular the Navier Stokes Equation, and would like to estimate the ...
2
votes
0answers
63 views

How to solve $y(x) y'''(x)=f(x)$

I have a PDE of the form $\partial_t y(x,t)+\partial_x(y(x) y'''(x)-f(x))=0$, where $f(x)=\cos(x)$. Suppose a stable equilibrium exists, and I want to find the steady-state solution $y(x) y'''(x)=f(x)...
2
votes
0answers
22 views

Difference between contraction rate and convergence rate

I am slightly confused about the concept of contraction rate. For me it sounds equivalent to a convergence rate. Could somebody clear up the difference for me? I have those two definitions of ...
3
votes
0answers
42 views

Is it Grid/Cluster/Cloud Computing? How are those terms defined?

There are three very connected and widely used terms: Grid and grid computing Cluster and cluster computing Cloud and cloud computing In many situations, it is not obvious which term to use, as I ...
5
votes
1answer
216 views

Stability of hyperbolic PDE and DG-FEM

In the book of Hesthaven and Warburton on discontinuous Galerlkin methods in example 2.3 (regarding solutions of the wave equation), the authors regard the following PDE: $$\frac{\partial u }{\...
0
votes
0answers
56 views

What are the differences between these different forms of equation?

What are the differences between Conservative differential form, Non-conservative differential form, Conservative Integral form and Non-conservative integral form of differential equations? I know ...
1
vote
0answers
46 views

How to get the derivatives of the determinant and inverse of 2nd-order tensor wrt itself in SymPy?

I have a second-order tensor for which I need to compute the derivatives of its determinant and inverse w.r.t. itself. The equations are as follows: $$\frac{\partial \, det(\mathbf{F})}{\partial F_{...
1
vote
1answer
112 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 ...
4
votes
1answer
185 views

DG-FEM integration by parts

I am going through the book of Hesthaven and Warburton on discontinuous Galerkin methods. I have difficulties understanding some basic steps in the calculations. Consider the PDE: $$\frac{\partial u}...
2
votes
1answer
127 views

Why my parallel code using MPI is much slower than the serial one?

I know that is not the first time someone asks this question but I'm really confused.I'm new to MPI, and I tried to implement the Jacobi solver for a linear system $Ax=b$. I want to compare the time ...
2
votes
1answer
116 views

Simultaneously maximize and minimize

I am virtually new to optimization (saw it years ago in a very shallow course) and now I came across a problem that I believe would require from it. The problem is I don't know exactly how to proceed. ...
1
vote
1answer
60 views

Abaqus, ANSYS, and FVM solver for thermal expansion problem converges to different values

Is it reasonable for a FEM and FVM code to converge to slightly different solutions for the same physical problem (identical BCs, geometry, properties, etc...), provided stability constraints are ...
2
votes
0answers
48 views

Reverse automatic differentiation and integration

In Symplectic Runge-Kutta schemes for adjoint equations, automatic differentiation, optimal control and more Sanz Serna writes: It is well known that the reverse mode of differentiation implies ...
0
votes
2answers
297 views

(FEM) 1D time-dependent heat equation convergence problem

I'm simulating a simple 3-node bar with convection BCs at the edges to validate my FEM code. The following data was used: Initial temperature = 25 ºC Temperature surrounding the rod = 10 ºC Thermal ...
3
votes
1answer
85 views

Optimality of block-Jacobi preconditioner

For a dense $N \times N$ matrix $A$, is the block-Jacobi preconditioner comprising the inverse of the diagonal blocks of $A$ the optimal block-diagonal preconditioner? Could there exist another matrix ...
1
vote
0answers
47 views

Kinetic preconditioning

Publication arXiv:0804.2583 describes a method for doing self-consistent iteration without having to diagonalize the Hamiltonian operator at every step. IX. PRECONDITIONING As already ...
2
votes
2answers
103 views

Interpolation vs. Neural network

I am seeking knowledge from the community. I am solving a transport PDE (conservation of solute mass) using COMSOL. At each Newton-Raphson iteration, I need to update a constant called $Kd$ for some ...
0
votes
0answers
26 views

A preconditioner for self-consistent iteration

I tried to derive a preconditioner for self-consistent iteration similar to section IX in arXiv:0804.2583. For simplicity, consider here only one orbital (one or two electrons) systems. Suppose that ...
2
votes
0answers
36 views

maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of elements ...
1
vote
0answers
83 views

Library for Discontinuous Galerkin method: FEniCS vs deal.ii

I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these ...
0
votes
0answers
28 views

how to estimate the number of people on a street within an hour?

I tried to use opencv to analyze a video filmed on the street. But the problem is the performance is not enough. I think the number of people must follow the poisson distribution. So I want to ...
0
votes
1answer
42 views

Find shift in high resolution noisy signal if only local argmax data are available

Let's say I have a signal which consists several pulses of approximately equal height, and I have to correlate it with the expected positions of the peaks to find the shift of this signal w.r.t. a ...
0
votes
0answers
68 views

Algebraic multigrid for coupled equations

As far as I understand is algebraic multigrid(AMG) a method that was intentionally developed to solve linear systems where every grid point or node has a single DOF. When AMG should now be used for ...
0
votes
0answers
38 views

Techniques to optimise the integral of a function of known analytical form

I need to compute repeatedly a function that depends on an integral. The integral is not solvable analytically, but it depends on the argument of the function parametrically, like this: $$ f(x) = \...
4
votes
2answers
81 views

GPGPU language for AMD?

Nvidia seems to be dominating the HPC / GPGPU computing landscape with CUDA. If I want to write a scientific application using and AMD GPU, what is the preferred language these days? I believe it used ...
3
votes
1answer
63 views

Whitening transformation does NOT return a unit covariance matrix

For this question, I am using the following Wiki definition of Matrix whitening: Suppose $X$ is a random (column) vector with non-singular covariance matrix $\Sigma$ and mean 0. Then the ...
15
votes
5answers
1k views

Why does the numerical solution of an ODE move away from an unstable equilibrium?

I wish to simulate the behaviour of a double-pendulum-like system. The system is a 2-degrees-of-freedom robot manipulator that is not actuated and will, therefore, behave mostly like a double-pendulum ...
2
votes
1answer
107 views

Calculate amount of FLOPs for an eigenvalue problem solver

I have 2 complex, non-symmetric, matrices $A_{1000\times1000}$, $B_{1000\times1000}$ and I am using Matlab to get it's eigenvalues (functions like eig or eigs). Both matrices are different - one is ...
3
votes
0answers
35 views

Derivative of Whittaker-Shannon interpolant

Last time we looked at how to improve the accuracy of Whittaker-Shannon interpolation, where user njuffa demonstrated that judicious use of sin_pi could greatly ...
0
votes
0answers
44 views

Need an example Legendre-Gauss-Radau pseudospectral differentiation matrix or Matlab code

I'm trying to implement various kinds of pseudospectral methods for direct optimization in Matlab using IPOPT. I've got some working Legendre-Gauss-Lobatto code, but would like to use the flipped ...
2
votes
0answers
29 views

How to solve the Poisson equation with KINK aligned with mesh facet

I have a problem that solving the Poisson equation with kink ( discontinuous gradient but solution is continuous ) in the analytical solution, I want to solve this problem with FEM. To approximate ...
3
votes
1answer
96 views

References for the nonlinear reaction-diffusion equation using Finite Element Methods

I want to study how to solve the following PDE \begin{cases} -\nabla \cdot(\ k(x,y) \ \nabla u \ ) + \beta(x,y)\ u^2 = f(x,y), \ (x,y) \in \Omega \subset \mathbb{R^2} \\ \hspace{0.5cm} u = ...
0
votes
0answers
57 views

Computing a double Integral using two Riemann sums & graphing multiple isosurfaces

I'm trying to compute the potential and electric field of a uniformly charged spherical shell and plot the results in the space outside the shell using MATLAB. I've tried everything from for loops to ...
3
votes
1answer
73 views

Geometric Programming - symbolic version

I am interested in finding minimizers of functionals of the type $\sum x^ay^bz^c$ where the exponents are 1, 0 or -1. I have codes to find such minimizers when they exist up to machine precision, ...
6
votes
1answer
88 views

Going back in time in an initial value problem

Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$. If I need to find $y(t^*)$, hence finding the path for $y$ in $t \in [0,t^*]$ and $t^*<0$; is the ...
1
vote
2answers
151 views

Order of element vs Degrees of freedom of the element

I have read that the order of the element is the order of the polynomial used to approximate/represent the field variable in that element. If we consider a one-dimensional, 2 degrees of freedom ...

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