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11 views

When semicoarsening is needed in multigrid method?

I am trying to understand multigrid in deep and all the coarsening techiques. So,assuming a 2D grid when semicoarsening is prefered instead of standard coarsening?What is the error's behaviour when a ...
0
votes
1answer
34 views

How suitable is multigrid method for time-dependent PDEs?

For elliptic PDEs (Poisson-type), the multigrid method is very sufficient, but how about time-dependent problems (i.e parabolic or hyperbolic PDEs)? Is it efficient to solve such problems using a ...
1
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0answers
21 views

Attempting to perturb ODE when initial condition is equilibrium point does not work

I have the following system of differential equations: $$ x' = ax- cy + e1 $$ $$y' = by- dx + e2 $$ for variables $x,y$ and parameters $a,b,c,d,e1,e2$. I'd like to solve this in python, which is ...
0
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0answers
7 views

Can we start Simplex method at a different corner than origin

I am working on a complex LP where I would like to get a fast heuristic solution and use it as a starting point for Simplex. The heuristic algorithm provides a corner point, but I am not sure how to ...
5
votes
3answers
230 views

Fast evaluation functions given by straight-line programs

I have a simple but long function that takes a vector x[10], and outputs a vector y[100]. It is an automatically generated eval function for a multivariate polynomial, ie, there is only (complex) ...
0
votes
1answer
66 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 ...
8
votes
1answer
137 views

Radial integration of expensive function with Bessel weights

I need to calculate the integral $$I = \int_0^R f(r)J_n\left(\frac{z_{nm}r}{R}\right)rdr$$ where $J_n$ is the $n^{\mathrm{th}}$ order Bessel functions of the first kind, $z_{nm}$ is its $m^{\mathrm{...
0
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1answer
45 views

Solve linear system with Newton-Raphson method

Is it possible to solve a linear matrix system $A x = b$ using the Newton-Raphson method? If yes, how can this be done? More special, how is the derivative build?
-3
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0answers
8 views

How to check the feasibility of a set of linear inequality constraint?

(The image of the whole problem is also included) Consider a set of linear inequalities constraint as: Ax >= b, 0 <= x <= L, where A(N,N), x(N,1), and b(N,1). It is assumed that the ...
1
vote
1answer
2k views

Divergence in COMSOL

I'm trying to calculate the divergence of a vector quantity $L(L_x, L_y, L_z)$ in COMSOL. I calculate it using the built-in differentiation operator as follow: $$\nabla L = d(L_x,x)+d(L_y,y)+d(L_z,z)$...
-1
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1answer
28 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. ...
3
votes
1answer
58 views

Scipy Spline Interpolation Parameter

Documentation in scipy.interpolate (found at https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html) states: "The parameter variable is given with the keyword argument, u, which ...
0
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0answers
27 views

Coding of density of states of a 2D square lattice in python [on hold]

I want to get python code for the calculation of density of states. I am very new on coding. Can anyone help me out this situation?
2
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0answers
19 views

How to deal with pseudo-compressibility of lattice Boltzmann method when you are calculating mass flux?

In lattice Boltzmann method, we have a concept, which is called pseudo-compressibility and it is defined based on the fact that LBM simulates incompressible flows by having small Mach number to ensure ...
5
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0answers
79 views

“Geometry of ill-conditioning” for least-squares problems

It is an idea that dates back to Demmel, 1987 that the condition number of a problem is often related to the distance to the closest ill-posed problems. In Section 3 of the above paper, the author ...
2
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0answers
42 views

Why wall shear stress calculated from LBM directly and the one calculated based on velocity profile are so different in some cases?

First of all, I hope you accept my apologizes if my question seems off topic here. But, I asked this question in ParaView forum and after a week still I did not receive any response yet, so I'm ...
-1
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0answers
14 views

Using Patchmatch for image inpainting

I've been reading over the Patchmatch paper and sample repositories and I understand what the algorithm does. It finds pairs of pixels between two images (or the same image) that have similar ...
1
vote
1answer
81 views

Numerical integration in 2D

I would like to solve the following problem $$ \vec{v}(x,y)= k\, \nabla \theta(x,y) $$ with respect to the unknown function $\theta$. Parameter $k$ is just a real constant quantity. I have two ...
0
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0answers
42 views

Problem with rate of convergent of numerical scheme for hyperbolic conservation law

I need help to verify my code in C++ that developed to solve the Burgers equation $$\\u_t + (\frac{u^2}{2})_x =0$$ $$u(x,0)=\sin(\pi x),\text{ } -1\leq x \leq 1$$ using a third-order ...
3
votes
1answer
53 views

Calculate Transformation Matrix between two sensors

My question is if I can calculate the transformation matrix between two sensors. Each sensor provides a $4\times 4$ matrix for every timestep recorded. The sensors are moving and have some noise in ...
0
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1answer
42 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 ...
2
votes
1answer
64 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 $...
0
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0answers
31 views

FEniCS, refinement not 'respecting' domain boundary

Short question: how to ensure that extra points are not included as 'boundary' points after calling the refine function. More details. I am working with a hexahedral mesh in $3$d. Let $X$ be the set ...
1
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0answers
37 views

Can the standard multigrid performance be used for time-dependent PDEs?

Consider a time dependent pde(i.e u(x,t)).I know when only space-coarsening is used the standard multigrid performance can be applied but what if instead we use only time-coarsening?Can we apply the ...
0
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2answers
6k views

How to prove the 2-norm of an invertible matrix is exactly the reciprocal of its minimum singular value?

If a matrix $A_{n\times n}$ is invertible, then $\left\|A^{-1}\right\|_2 = \dfrac{1}{\min\limits_{i} \sigma_i}$ where $\sigma_i$ is the $i$-th singular value of $A$
1
vote
0answers
66 views

understanding Domain Decomposition with example

I am new in Domain Decomposition method. I am started to solve $-\Delta u = f$ in $\Omega$ and $u = 0$ on $\partial\Omega$. From that I get in $\Omega _1$ $$\begin{bmatrix}4&-1\\-1&4\end{...
3
votes
1answer
54 views

Differences between Discrete Fourier Transform and Continuous Fourier Transform?

I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...
2
votes
2answers
70 views

Chebyshev differentiation via FFT with a domain [a,b]

I want to ask something about Chebyshev differentiation via FFT, which can be used to obtain with spectral accuracy the derivative of a smooth function. See for instance this code in python, which ...
1
vote
1answer
247 views

ODE Solving in Scilab

I have a certain ODE problem that needs to be solved using Scilab. dx(1)/dt=k*x(1)-x(5) dx(2)/dt=k2*x(2)-k1*x(1) dx(3)/dt=k1*[x(2)-x(3)] dx(4)/dt=k1*[x(3)-x(4)] <...
1
vote
1answer
43 views

Matrix multiplication not working in Scilab

I entered an instruction to calculate the coordinates of a vector after a change of basis in order to repeat it many times with various vectors. X0=[1;1/2] is a ...
3
votes
1answer
330 views

General case Kutta condition

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
7
votes
1answer
115 views

Numerically estimating expected value of f(x) when x is normally distributed

I need to estimate $$ \mathbb{E}_x[f_i(x)] = \int_{\mathbb{R}^n} f_i(x) p(x) dx $$ for many functions $f_i(x)$, where $p(x)$ is the density of a normal distribution. The evaluation of all the ...
1
vote
2answers
132 views

Lattice Boltzmann methods vs Navier stokes/ other eulerian methods for *water* simulation

Note, there is already a question here, however the answers don't answer the original question, let alone specific considerations when dealing with nearly in-compressible fluids (water). Another ...
1
vote
1answer
75 views

Eigenfaces Algorithm

This might be a silly quesntion but recently I've been trying to program the eigenface algorithm using PCA, so I arranged the face vectors vertically in a matrix X such as: X = [x1,x2,x3,...,xn]; In ...
2
votes
3answers
91 views

How the gmres method iteration behaves for this **enfant terrible** matrix?

Recently, I have been studied my lessons about gmres iteration, probably the most popular iteration method for general large sparse linear system of equations Ax=b. And the convergence is obtained ...
2
votes
2answers
59 views

Can a direct method like Thomas be used in a multigrid method as a smoother?

As far as I know, multigrid uses stationary iterative methods as smoothers (i.e GS), but can we use a direct method also? For example, in case we have a tridiagonal system (for example 1D heat ...
2
votes
1answer
47 views

Partially Banded Matrix

I have a somewhat peculiar Jx=R system that I need to solve. The matrix J is 2N -by- 2N. The first N rows have all entries filled. The next N rows are banded in two places, i.e. for the (N+k)th row, ...
1
vote
1answer
31 views

Accelerating Conjugate Gradients fitting for small localized kernel (like cubic B-spline)

Question: Is there some pre-conditioner for Conjugate-Gradient (CG) cheap enough, that it is worth using even if my operator is very local (i.e. already has a low number of non-zero elements), as it ...
1
vote
1answer
62 views

Simulating advection - diffusion problem in a network of 1D pipe

I'm interested in solving the following advection-diffusion system in a 1D network of pipes. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$ ...
3
votes
1answer
101 views

Solving an SDE with time-dependent parameter in R

I am trying to solve a system of SDEs in R using the Diffeqr package. Let's reduce the system to a simple ODE: ...
1
vote
2answers
378 views

Correct use of scipy's sparse.linalg.spilu

I'm attempting to use scipy's spilu routine as a preconditioner and I'm finding bad performance for my application (solving a global linear system arising from a DG ...
2
votes
1answer
139 views

A Bound for the inverse of the sum of identity and triangular matrix

I wonder if there are any theorems which can help me to calculate an upper bound for the spectral norm of: $$\left\| \left[ I + \sum_{i=1}^{\overline{n}\in\mathbb{N}} \big( C_i - I\big)\right]^{-1}\...
-2
votes
0answers
17 views

Asymptotic Analysis Proof using Domain and Range Transformation [closed]

I was wondering if you guys could help solve the proof (it's a time complexity problem, and I needed to use Domain and Range Transformation. I used Master Theorem, but my professor also said to use ...
5
votes
1answer
57 views

How to record hardware and software info in Julia?

Watermark extension for Jupyter shows system and package information for reproducibility: ...
2
votes
1answer
93 views

Eigenvectors associated to two quasi-degenerate eigenvalues

I need to find the smallest eigenvalue and the corresponding eigenvector of a sparse matrix $M$ whose dimension is $\approx 10^4$. Within Matlab enviroment, I use the command ...
0
votes
1answer
48 views

Method to calculate solution of a linear equation system?

I am searching a solution method for the following equation system of equation systems: Let $A, B \in \mathbb{R}^{n \times n}$ be s.p.d. Matrices and $O$ be the zero matrix of the same size. Further ...
2
votes
1answer
74 views

Step size and stability of Euler forward method

I'm trying to calculate the maximum step size that provides stability for the following nonlinear IVP using the Euler forward method: $u'(t) = -200tu(t)^2,\qquad u_0 = 1, \qquad t\in [0,3]$, with ...
0
votes
2answers
39 views

What's the difference between the 2 ways of definitions of function handle? which is robust and better?

Recently, I have been studying Krylov subspace iterative methods. I find the matlab robust command pcg and the new concept of the function handle to return a matrix-vector product. Then I use help pcg ...
6
votes
3answers
326 views

Does a symmetric positive definite matrix also have $\mathbf{A} = \mathbf{L}^T\mathbf{L}$ (where $\mathbf{L}$ is a lower triangular matrix)?

As we know, for a symmetric positive definite (SPD) matrix $\mathbf{A}$, there is a theorem about the Cholesky factorization $\mathbf{A}= \mathbf{L}\mathbf{L}^T$, where $\mathbf{L}$ is a lower ...
0
votes
0answers
23 views

Why does the matlab command **chol(A)** slower than **chol(A,'lower')** for a large sparse SPD matrix?

For a SPD matrix A, there exists Cholesky factorization $A=LL^T$ or $A=R^TR$, where L, R are a lower and upper triangular matrix, respectively. Also in matlab, there has a command R = chol(A) which ...

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