Questions tagged [grid]
For questions about solving numerical problems by evaluating over a discrete grid of points in the problem domain.
56
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Approximation of an integral over a grid of given values in R
Suppose that $f()$ is a mixture of two exponentials which is given by:
\begin{equation}
f(x; \Theta) = w_1 \lambda_1 e^{-\lambda_1 x} + w_2\lambda_2 e^{-\lambda_2 x},\; x> 0
\end{equation}
I aim to ...
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50
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A staggered grid for an eigenvalue problem (linear stability analysis)
I'm interested in extending the concept of a staggered grid (commonly used to solve the incompressible Navier-Stokes equations) to a linear stability analysis context. For example, we can consider ...
- 11
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28
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boundary condition at rotation axis of a spherically-symmetric system
The quantity I am interested in is not the rotation rate $\Omega$, but I will use this quantity nonetheless to make the problem clearer. I am interested in a spherically-symmetric system and in the ...
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28
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Grid search for bi-level optimization
Apologies if this isn't the best place to ask this question, and further apologies for such a basic question (I am a secondary school graduate and have not learned very much yet). Please direct me to ...
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1
answer
69
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Choice of grid generation for FDM discretisation methods
I'm currently revisiting some FDM schemes for convection-diffusion equations in 1D, 2D and 3D and getting up to speed with the industry-standard methods again. The application is derivatives pricing, ...
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43
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How to choose MPI topology for uniform 3D Cartesian grid that is not cubical?
When writing an MPI-parallelised code, I need to split a global Cartesian domain of $(N_x, N_y, N_z)$ cells among $M$ MPI ranks. For simplicity, we can assume that the decomposition is "simple&...
- 101
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50
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Centered finite volume scheme for an advective term on an unstructured/irregular/non-uniform grid
Consider the continuity equation
$$\frac{\partial u}{\partial t} + \frac{\partial \Phi}{\partial x} = 0$$
$$\Phi = au + b\frac{\partial u}{\partial x}$$
Suppose I want to solve the above using ...
- 297
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50
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Multigrid/Two-grid method restriction and prolongation of residual
Starting from the problem $Au=f$, I'm not sure that I understand why a coarse grid solution is implemented on the coarse grid residual $r_c^{(k)}=P^Tr^{(k)}$, with $r^{(k)}=f-Au^{(k)}$ and $P^T$ ...
- 109
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1
answer
43
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An explanation of 2delta waves on non-staggered grids
While looking into the difference between staggered and collocated grids, I came across an effect called $2\Delta x$-oscillations, which happen on non-staggered grids, but not on staggered grids. This ...
- 105
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1
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67
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Restriction in (geometric) multigrid for vectors of non-even length
Naive restriction operators in geometric multigrid that I have seen are typically implemented as a convolution and a subsequent averaging of every two entries in a vector $v^h$. For example:
$$\tilde{...
- 621
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188
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Calculations on discontinous grids
Suppose for a grid-based calculation a grid is used such that the grid Jacobian is discontinuous. For example, in 1D, for a domain $x \in$ [0,1], one half of the domain is covered uniformly by twice ...
- 2,230
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Is there any reliable free/open source tool for structured mesh smoothing?
I have been using Pointwise for grid generation and found the quality of smoothed grids to be stunning.
I am not aware of any free/open source alteranative that offers the same capabilities for ...
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1
answer
152
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Overlapping 1D grids
I have two 1D grids, each of them is a finite collection of cells, where the cell is defined by the left end and the right end, $[cell]_{i}$=$[x_{i}^{left}$,$x_{i}^{right}$]. I need to find the ...
- 2,230
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353
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How are finite volume method boundary conditions implemented without using ghost-cells?
I'm currently trying to implement my own FVM code in cpp, but when I try to calculate the laplacian of a test function, given by
\begin{align}\phi_0=\sin(2\pi x)\sin(2\pi y),\end{align}
I get ...
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1
answer
32
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can you give me some information of tools for load reblance
I want a tool for load rebalances.
I have a distributed grid. Each process can handle a part of the global grid. Each process has a different node and I want to rebalance it. I want a tool that can ...
- 333
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votes
2
answers
80
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How to refine the tetrahedron if exist two longest length edge?
In some algorithms to refine tetrahedron, we need to calculate the longest edge.
background
If exist a tetrahedron with node ABCD, it has edges ...
- 333
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2
answers
177
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What makes a good computational grid?
Most computational methods for solving PDEs are grid-based. What makes a computational grid "good", other than being sufficiently fine to resolve features of numerical solutions? Are grids ...
- 2,230
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2
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103
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Grid Independence Study
Is the change in time step necessary for the grid independent study? As the CFL is based on the relation between dt and dx.
In mesh independent study, only change should be mesh i.e, dx isn't it so?
- 11
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147
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What is the reason for this finite-difference high errors on non-uniform grid?
tl;dr
Using a Taylor-matched method to find coefficients for the discretized equation $ \mathbf{A} \vec{f}'' = \mathbf{B} \vec{f} $, a Fortran code has been implemented to find the second derivative ...
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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 ...
- 417
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0
answers
31
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Solution errors when refining a static grid: Continuous vs. step-wise refinement
Let's assume I am working on a 2-D domain on $R^2$, with my coordinates $x \in[-1,1]$, $y \in[-1,1]$ and I want to solve a popular CFD problem, like the shallow water system or the Euler system.
At $x=...
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0
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Grids for atmosphere simulation with finite volumes on the globe
I am currently in the early construction process of building a simple CFD model of a rotating planetary atmosphere. The planet should be allowed to tilt significantly, so that a time-dependent source ...
0
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1
answer
259
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Good C, C++ library for efficient grid search / tuples, ideally with bindings to Eigen
I have a $q$-dimensional grid, known at run, not compile-time, that has $50$ points in each direction and hence $50^3$ combinations that I would like to first build and then call a function with each ...
- 183
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answers
19
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Translating grid with extrusion speed
I am putting into MATLAB code the equations that describe a plastic extrusion process. From a paper, I found I should use a spatial grid that translates with the extrusion speed, being the reference ...
- 11
3
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answers
146
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WENO5 scheme in a staggered grid
I'm trying to use the finite-difference WENO scheme to solve the 2D density conservation law with axial symmetry (coordinates $r,z$):
$\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho \vec{v}) = \...
- 141
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vote
1
answer
376
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Mapping derivative information in uniform to non-uniform grid
I'm having two sets of grids. One is uniform and another one is not uniform. I will calculate the derivative in uniform grid points and I like to transfer(map) the derivative to the non-uniform grid ...
- 514
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1
answer
119
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Grid dependence of a numerical model
Statement of the problem
Suppose, we consider the following model
$$
\begin{array}{l}
(1)~\mathbf{u}_t + \mathbf{F(u)}_x = \mathbf{S}(\mathbf{u},\mathbf{w}), \\
(2)~\mathbf{w}_x = \mathbf{P}(\mathbf{...
1
vote
2
answers
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Access optimized data structure for representing integer lattice
Consider the integer lattice in $2d$, namely the set $\mathbb{Z}^2 = \{(x,y): x,y\in \mathbb{Z}\}$, and let $u:\mathbb{Z}^2 \to \mathbb{R} $ be a function defined on some bounded subset of $\mathbb{Z}^...
- 111
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1
answer
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Three dimensional irregular grid data interpolation to regular grid
I have three-dimensional radar reflectivity data obtained as voxels (scans, rays, altitudes). The data has been sampled at irregular spacings and I want to convert this into a regular grid. In ...
- 215
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1
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50
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Converting mass density to point mass approximation on a grid
In an nbody gravity simulation, instead of doing exact(all-pair brute force) solution, I added masses of each body into cells of a 3D grid(each cell is just a float value having a mass value). Then ...
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answers
156
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Choice of velocity grid - staggered or not?
I'm trying to understand when and why one would use a staggered vs. a colocated grid in problems that have velocities and scalars that they transport (e.e. density).
If scalars are defined cell-...
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0
answers
70
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adaptive / smart grid choice for dynamic programming
I've a read a paper about investing where they used a dynamic programming approach to solve a finite horizon problem, i.e.
$$\max_{x_t} E[u(W_T)] $$
where $u$ is a utility function and $W_T$ ...
- 101
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vote
2
answers
180
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Grid mapping from Tchebyshev
I am using Tchebyshev discretization to solve a system of PDEs.
Usually, I map the Tchebyshev space($\xi$, from -1 to 1) to physical space ($x$, from 0 to L) using $$x = (\xi +1)*L/2$$
Now, I also ...
- 133
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2
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Efficient Representation of (spatially sparse) spatial time series
Background
I have a huge dataset consisting of points (on a plane) together with a timestamp for each point. This is a collection of car GPS measures, giving us the location (latitude/longitude) of ...
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answer
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Balancing core load when number of particles in cells vary (PIC on GPU)
Consider this basic scheme for particle in cell simulations ( with just short-range interactions ):
assign particles to disjunct cells
for cell $A$ go over neighboring cells $B$
for each particle $...
- 907
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vote
1
answer
510
views
Finite Volume Polar Discretization: Lengths
Given a uniform polar grid, as in the figure below:
and a FV discretization of a gradient for example:
$\frac{\partial p}{\partial \varphi} = 0$
$\Delta r \frac{p_e - p_w}{\Delta \varphi} = 0$
My ...
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0
answers
186
views
How to optimally choose points for multivariable Hermite interpolation?
I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input.
I would like to create interpolation polynomial for it.
In one-dimensional case ...
- 193
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2
answers
1k
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Finite Difference Grid Spacing and Scaling
I have been exploring finite differences and heat transfer using the 2D heat equation to further expand my knowledge. So far I think it is going well.
I am running into some confusion around grid ...
- 11
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vote
1
answer
3k
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Is there an advantage of using a staggered grid over a regular one when combined with high order methods?
The title says is all. This question is in the contest of an incompressible Navier-Stokes solver.
Specifically, I am currently working on a new solver while referring myself to an older code for ...
- 337
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votes
1
answer
1k
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Interpolation of velocities on staggered grid (in PIC)
Edit: (copying from my comment)
Let's consider the inverse problem when I need to transfer velocities from particles to the grid (inverse bilinear interpolation). How'd I transfer a particle's x-...
- 185
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vote
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answers
168
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C1 continuous spline on regular 2D-grid with quadratic 1D cuts
I want some scalar spline function defined on regular 2D grid $F(x,y)$ with continuous first derivative which is easy to intersect with arbitrary ray/line ${\vec l}(t) = (c_x t,c_y t,c_z t)$.
...
- 907
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votes
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135
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Alternative to messy grid node indexing within multiple layers of loops
Recently,I dive into a set of somehow ancient Fortran codes and try to fully understand them. A large fraction of these codes are multiple layers of loops over many state variable dimensions, which ...
- 131
1
vote
1
answer
677
views
3-dimensional plotting with nonuniform grids
I have 3 variables I am considering: time (t), 1-dimensional space (x), and intensity (I). I would like to plot the intensity in the z-axis as a function of t and x (the latter two variables would ...
- 568
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votes
1
answer
2k
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Contour plot interpolation recommendation
I am not sure if my question is on topic or not and if not please let me know. I have regularly spaced gridded data(output of a weather forecast simulation software) and I have latitude and ...
- 215
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0
answers
141
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Finding boundary intersection points with Cartesian grid?
I would like to find the intersection points e.g. $M_x$ and $M_y$ as in the attached figure. The boundary (solid line) is defined by the Lagrangian points.
I am working in C++ (basic - medium ...
- 25
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vote
1
answer
100
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Common nodes in two FEM grids
There are two independent tetrahedral FEM grids. Second grid is subset of the first. By subset, I mean: nodes from the second grid are exactly in the same positions as some nodes from the first grid. ...
3
votes
1
answer
2k
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Generating a non-uniform grid
I am interested in generating a 1D non-uniform grid on the interval [0, L] with N points, where a region of width $\sigma$ and ...
- 265
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1
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1k
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Quadtree type Grid
I would like to code for a quadtree type meshing but don't know how to do. If anyone can help or can share any starting code?
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votes
5
answers
12k
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Dynamically ending ODE integration in SciPy
I have a light ray moving through space-time, i.e. a curve in $\mathbb{R}^4$, parametrized by some variable λ. The exact trajectory, i.e. the coordinate functions $x^μ(λ)$ of the curve are given by ...
- 243
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68
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Should I use bestman2 or dcache CLIs (srmping, srmls, etc..)
I am fairly new to using SRM, and I am wondering if I should be using srm CLI tools (srmping, srmls, srmcp, etc..) provided by dcache, or bestman2 counter parts (srm-ping, srm-ls).
I used to think ...
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