Questions tagged [grid]
For questions about solving numerical problems by evaluating over a discrete grid of points in the problem domain.
49
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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 $P^T$ ...
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1
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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 ...
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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{...
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1
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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 ...
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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
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103
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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 ...
- 1,969
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202
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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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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 ...
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2
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77
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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 ...
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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 ...
- 1,969
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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?
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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 ...
- 407
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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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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 ...
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207
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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 ...
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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 ...
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126
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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}) = \...
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1
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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 ...
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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{...
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2
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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}^...
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1
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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 ...
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1
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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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147
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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
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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 $W_T$ ...
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2
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173
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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 ...
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votes
2
answers
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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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1
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51
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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 $...
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424
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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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179
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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 ...
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2
answers
930
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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 ...
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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 ...
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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-...
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158
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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 ${\vec l}(t) = (c_x t,c_y t,c_z t)$.
...
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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
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1
answer
633
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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 ...
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1
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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
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134
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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 ...
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1
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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
1k
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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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997
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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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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 ...
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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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1
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How to compute the weight matrix for tomography applications?
I am trying to compute the weight matrix for a set of straight ray paths through a reconstruction region.
Ideally, I would like to be able to do this for both a rectangular grid region, where each ...
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1
answer
34
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How can I discover / access various SE (storage elements) in GlideinWMS environment?
I am submitting jobs to Open Science Grid from a glidein-wms enabled submit hosts such as osg-xsede. I'd like to stage some data on SE nearest to osg-xsede submit host, then distribute data to various ...
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1
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2k
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Python: Grid with step control ODE solver
I have a problem in physics formulated via an ODE. Now I like to solve it numerically using Pythons scipy.integrate and the therein complex_ode. I figured out how and it works but now I like to ...
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Ray tracer : create an uniform grid [closed]
I wrote a simple ray tracer, and now I try to implement an uniform grid. There is a lot of documentation on how to traverse the grid, but I don't know how to construct the grid.
I have my uniform ...
- 11
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1
answer
149
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How to convert a Matrix to a DistMatrix in Elemental?
I have a Matrix<double> on a single core, the result of doing an MPI_Reduce. I want to do the Cholesky, so I need to ...
- 373
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1
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52
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Cells segregation
There is unstructured grid which contains only quadrangles cells. Each cell has 4 neighbors, and known them (has a pointer to them). I can iterate through all cells in the grid. Some cells are marked ...