# All Questions

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### 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 ...
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### 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 ...
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 ...
32 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 ...
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 ...
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. ...
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?
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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### What is appropriate boundary condition for Poisson pressure equation?

I'm doing CFD simulations in unstructured grids. Well, it's a bit different from conventional unstructured grids that are used mainly in FEM or FVM as tetrahedral meshes. Mine is a voxelized mesh of ...
90 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 ...
62 views

### How can I calculate the exponential integral?

(I originally asked this in a different exchange.) I'm writing a program that uses the prime-counting function. Right now, I'm using x/log(x), but I want to ...
22 views

### Solving a system of PDEs with no-flux boundary conditions (finite difference discretization)

I am interested in solving a system of linear PDEs with the finite difference method and I'm having trouble to solve the no-flux boundary condition correctly. \begin{align} \frac{\partial n}{\partial ...
19 views

### Speedup of CPU Pipelining by number of steps

When a CPU has $K$ steps the speed up of using pipelining compared to non-pipelining is $K$. But what I want to know is, say I am a CPU designer and want to decide whether I should build $K$ or $N$ ...
31 views

### How can I determine if there is a closed-loop path in a graph?

Assuming I have a computer representation of a graph presented in the figure below: How can I find out whether there are some close-loops inside the graph, like the one marked in red (or more ...
37 views

### Can we use interpolation function of different order to represent different degrees of freedom in a FEM element?

Consider a line element in FEM. Let each node have 3 DOF. They are x and y translation DOF and temperature. Can we use interpolation functions of different orders for the translation DOFs and ...
62 views

### How to compute all the eigenvalues of a large sparse matrix using matlab?

In matlab, there are 2 commands named "eig" for full matrices and "eigs" for sparse matrices to compute eigenvalues of a matrix. And eig(A) computes all the eigenvalues of a full matrix and eigs(A) ...
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### 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 ...
26 views

### Symmetric sparse direct solvers in scipy

scipy.linalg.solve, in its newer versions, has a parameter assume_a that can be used to specify that the matrix $A$ is symmetric ...