Questions tagged [projection]
For questions about implementing mappings from a set of elements (points, vectors, etc) to some subset of these elements.
46
questions
1
vote
0
answers
29
views
How to find the formula of a projected circle in a pencil of conics structure?
Hi this is my first question on the platform so feel free to comment if I have a mistake regarding the question.
I'm working on an ellipse detection scheme in which I have markers consisted of 3 ...
1
vote
0
answers
93
views
From 3D to 2D with a STL file
I would like to do a 2D projection from a 3D geometry saved in a stl file and know the distance between the two projected planes. In order to explain better the concept I will start with an almost ...
- 99
0
votes
1
answer
103
views
How is the integral of a projection over an element $T$ computed in practice? (deal.II related)
I'm studying an error estimator for the equation $\nabla\cdot(\beta u) + cu = f$ and it contains the following term $$||f - cU_h - \Pi(f-c U_h) ||_T$$
where :
$\Pi$ is the local orthogonal $L^2$ ...
- 241
0
votes
0
answers
162
views
Do the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and reinversion) commute?
I try to check the equality or the inequality between 2 Fisher matrices.
The goal is too see if the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and ...
user14831
1
vote
0
answers
60
views
Why does including the pressure in this FVM for Stokes 2nd Problem lead to wrong solutions?
I'm trying to learn how to use finite volume methods and I want to solve a more general case of Stokes' second problem i.e. an infinite half-plane oscillating harmonically with no-slip boundary ...
- 136
6
votes
1
answer
243
views
Projection method FVM poisson part, adding source term
The idea of the method is to decompose the Navier-Stokes equation into the solenoidal and irrotational parts.
$$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$
...
- 364
0
votes
1
answer
50
views
Projecting nodal solution to gauss points with certain accuracy
I am having a problem that was also mentioned at the accepted answer to this question by Wolfgang Bangerth. I need to calculate, as it was specified at the question at the link, F1 integral and for ...
- 3
1
vote
0
answers
194
views
Lumped mass matrices for higher-order finite elements for CFD
Given that some of the mass lumping techniques, for example, row-sum lumping does not produce practically viable lumped mass matrices for all the element shapes, what are the techniques used for mass ...
- 865
2
votes
1
answer
196
views
Efficiently compute a projection matrix from Householders reflectors
Let $A \in \mathbb{R}^{m \times n}$ where $m \geq n$.
Let $B$ and $\tau$ be the result of applying LAPACK's dgeqrfp method (R on the upper right triangle, and the ...
3
votes
1
answer
190
views
Project to nearest point on convex polytope
I have a point $y \in \mathbb{R}^d$ and a convex polytope $\mathcal{P}$ given as the intersection of half-spaces:
$$\mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \le ...
- 390
1
vote
0
answers
100
views
Stokes problem with imposed acceleration on boundaries (projection scheme)
I am trying to solve FSI problems with finite elements and using a projection scheme (I am taking as reference the review of Guermond:
Guermond, J. L.; Minev, P.; Shen, Jie, An overview of ...
- 11
2
votes
1
answer
85
views
How to robustly and numerically expand a $k$-order polynomial in two variables defined on a polygon domain?
Given a $k$-order polynomial in two variable $p(x, y)$ defined on a polygon domain $K$. And I want to numerically expand it to the following form
$$
p(x, y) = c_0 + c_1 x + c_2 y + c_3 x^2 + c_4 xy + ...
- 143
2
votes
2
answers
100
views
projective reconstruction from orthogonal views
This is a problem from projective geometry. Suppose I have a vector $z \in R^k$ of unit length $\| z \| =1$ inside a $k$-dimensional hypercube. I don't know its value but do know its projection upto ...
- 203
2
votes
1
answer
485
views
Projection onto the set of Orthogonal matrices
Let $M \in \mathbb{R}^{n \times n}$ and denote the set of Orthogonal matrices by
\begin{equation}
\mathcal{O}_{n} = \left\lbrace Q \in \mathbb{R}^{n \times n} \colon QQ^{T} = \mathbb{I}_{n} \right\...
- 121
2
votes
0
answers
78
views
Geometric interpretation of lemma
I am currently studying eigenvalue problems. I already worked through the minimax-principles and seen why $\lambda_{h, m} \geq \lambda_m$, when comparing the eigenvalues of a discretization and the ...
- 155
5
votes
0
answers
79
views
Padua-type pointset for functions singular on line $x=y$
The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail here. With some work they can be used to generate a ...
- 2,125
0
votes
1
answer
73
views
Wanting an explanation of the variables in Iterative PCA algorithm
I've been trying to implement the CPU GS-PCA algorithm in this paper .
The code starts on page 28
I have a program written a script in python which gives the same output as the C++ program in the ...
- 257
1
vote
1
answer
134
views
Questions about iterative projection methods in Saad book
I am reading Chapter 5 of Saad's iterative methods book, and I don't understand section 5.2.1 about the two propositions of optimality results.
In the statements of the propositions, what does it mean ...
- 659
1
vote
0
answers
87
views
Stable Method of orthogonal projection onto a subspace with the help of Moore-Penrose inverse,
Projection of a vector $v$ onto the column space of a matrix $A$ is given by $AA^\dagger v$. From the definition of Moore-Penrose Inverse we know that $AA^\dagger v = (A^T)^\dagger A^T v $.
Below is ...
- 41
3
votes
0
answers
138
views
Backward stable algorithm to get orthogonal projection onto the column space of a matrix
I have to find the orthogonal projection of a vector $b$ onto the matrix $A$ of size $m \times n$.
In my application, I don't have the luxury of calculating the QR factorization. All I have are ...
- 41
4
votes
3
answers
905
views
How can I make sure the flow is divergence-free when I use moving mesh?
I am using projection method and P2/P1 finite element method to solve the incompressible Navier-Stokes equations while the mesh is constantly adapted as the body moves (edge swapping, splitting and ...
5
votes
1
answer
112
views
$L_2$ projection with integer constraints and prescribed sum
Suppose I am given a vector $v^0\in\mathbb{R}^n$ and integers $k,\ell\in\mathbb{Z}$. Assuming $k$ is close to zero (e.g. $0\leq k\leq5$), is there an algorithm for solving the following integer ...
- 1,341
1
vote
0
answers
100
views
How does this Constrained Minimization algorithm work?
I don't fully understand the subsection 3.2 Constrained minimization of this paper. In particular, I don't understand the first step "Register active set" and the definition of projection $P(x)$.
...
- 175
5
votes
2
answers
693
views
Efficiently removing projection to subspace without having an orthogonal basis
I have a number of vectors $v_1, …, v_n$ and another vector $w$, that all are linearly independent, but not orthogonal. Let $V := \mathop{\text{span}}(v_1, …, v_n)$. I need to remove $w$’s projection ...
- 2,022
2
votes
1
answer
261
views
Minimizing linear objective on intersection of convex sets
Suppose I wish to solve the following optimization problem:
$$
\begin{array}{rl}
\min_{\mu\in\mathbb{R}^n} &\mu^\top c\\
\textrm{subject to} & \mu\in C_1\cap C_2\cap\cdots\cap C_k,
\end{array}
...
- 1,341
0
votes
1
answer
100
views
Regarding solution vector of the wave equation
I am simulating the wave equation using FEM. For a 2D wave equation, when I visualise my output in Paraview, I see a separate solution in 'x' and 'y' direction for each node on the mesh. Therefore, if ...
- 347
1
vote
0
answers
343
views
How to obtain projections from sinogram in ART reconstruction technique?
I'm kind new in the Computed Tomography field and I'm trying to understand and implement ART technique. Said it, I started to read the book The Mathematics of Medical Imaging - A Beginners Guide by ...
1
vote
0
answers
93
views
Oscillations in Chorin's method due to the BC
I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
- 145
3
votes
2
answers
260
views
Implicit projection method with inflow boundary conditions
I am trying to use a projection method that deals with the viscous effects implicitly to model flow around a cylinder. I'm having trouble figuring out what the boundary conditions should be, ...
- 615
1
vote
0
answers
38
views
BC's for intermediate velocities in Implicit Fractional Step Methods
Lately, I was reading some seminal papers on Fractional Step Algorithms and I found this one:
Kim, D., Choi, H. A Second-Order Time-Accurate Finite Volume Method for Unsteady
Incompressible Flow on ...
- 251
2
votes
1
answer
142
views
Projecting a vector field onto a H(div) space
I've got a uniform quadrangular mesh and for each node there's a vector quantity $u$ defined. I also have a non-aligned material interface across the mesh. Now I need that vector quantity to have a ...
- 601
1
vote
1
answer
45
views
How to compute $\mathrm{proj}_{SDP}(C\odot X)./C$ without numerical problems?
I have a matrix, $X$, it is symmetric. I project $C \odot X$ and $D\odot X$ to semidefinite cone. $C$ is a Gramian matrix with some elements near zero and of course semidefinite, with one row and ...
- 221
7
votes
1
answer
151
views
Approximation properties of FEM projections operators on a boundary
We have an elliptic projection
$$P: V \rightarrow V_{h}$$
which satisfies
$$\Vert u - Pu \Vert_{L^{2}(\Omega_{e})} \leq Ch^{k+1} \enspace .$$
Can we say anything about $\Vert u - Pu \Vert_{L^{2}( ...
- 71
2
votes
0
answers
162
views
How to obtain the reduced model from a subspace projection method?
I have a system of ordinary differential equations (ODEs). It is a large system that has dozens of equations and hundreds of parameters. I wish to reduce its size so it becomes computationally more ...
- 121
2
votes
1
answer
180
views
How to project a 0 genus mesh model on a sphere?
I have a mesh which represents a 0-genus model. My goal is to construct a homeomorphism from that mesh to its bounding sphere.
I'm trying to understand a paragraph in http://citeseerx.ist.psu.edu/...
- 203
5
votes
2
answers
1k
views
Incompressible Navier-Stokes equations: Is projection method exact?
Is the projection method of integrating Navier-Stokes equations exact?
Take the incompressible flow equations:
$$
\frac{\partial\mathbf{u}}{\partial t} = -\mathbf{u}\cdot \nabla \mathbf{u} -\nabla ...
- 452
6
votes
1
answer
771
views
How to project a vector into the H(div) space (in the context of finite elements)?
Say I have a simple elliptic PDE:
$$
-\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega
$$
with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to ...
- 937
3
votes
1
answer
387
views
Active Elements in Projected Newton's Method?
To those who are familiar with the projected Newton's method or projected gradient method...
We consider a constrained optimization problem with simple bounds. Particularly, minimize f(x) subject to ...
- 81
10
votes
5
answers
3k
views
Motivation behind Galerkin method
I have a question about Galerkin method. I don't understand why the Galerkin method weights the residual by the shape functions and sets it equal to zero. I want to know what is reason of this. Why we ...
- 101
2
votes
0
answers
342
views
Treatment of Neumann (Traction) boundary conditions using projection methods
I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity:
$\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$
...
- 21
4
votes
2
answers
2k
views
Projection Method: Boundary condition on intermediate velocity field
I'm trying to solve variable density and viscosity Navier-Stokes equation using lagged pressure projection method. I'm solving for cavity problem as a test case now (once I get projection right, I ...
- 309
2
votes
2
answers
376
views
Projection of vector field on to a gradient field
Say I have a vector field with non-zero curl, therefore the potential function depends on the path I choose to integrate.
In this paper the authors proposed to project the vector field into a gradient ...
- 1,019
1
vote
0
answers
64
views
Mass-conservative reprojection (on a sphere)
I have a 2D distribution of mass on a sphere given as a matrix of masses in latitude-longitude grid cells. I need these masses projected to another grid
on the same sphere with different location of ...
- 111
1
vote
1
answer
1k
views
Lid driven cavity flow problem to solve with the help of projection method and use coding in fortran 90 [closed]
I want to solve Lid driven cavity flow with the help of projection method i want to make own fortran program to solve two dimensional unsteady flow.
I propose to solve the equations in the following ...
- 11
5
votes
0
answers
707
views
Generating pseudo-random orthonormal bases for random projection
I am performing series of random projections i.e. projecting the input matrix onto randomly generated orthonormal bases (of much lower dimensionality). The projection is just a matrix multiplication ...
- 151
3
votes
2
answers
1k
views
How to properly use polynomial projection to get values at visualization nodes?
I am trying to implementing a nodal discontinuous Galerkin spectral element method for linear and non-linear systems of equations. The solution at each time step is given at ...
