5
votes
Accepted
Common nodes in two FEM grids
Hashing floating-point numbers can indeed lead to weird results, especially if the node positions can be perturbed by some small amount or if there are denormalized values.
You included the Python ...
- 9,813
5
votes
What makes a good computational grid?
From a performance view, you are always interested in preserving as much 'structure' in your grid as possible. Computations on a simplex- or a hexaedral mesh, where every cell looks like the next will ...
- 2,621
4
votes
Accepted
Grid dependence of a numerical model
Your numerical solution is probably just getting more accurate as you increase the number of grid points. Do you know or have you tried to derive the analytic (exact) solution for this problem? By ...
- 343
4
votes
Accepted
Generating a non-uniform grid
You achieve this with equidistribution to a mesh density function $\rho(x)$.
If you consider $x$ as a continuous map from $\xi \in [0,1]$ into your domain $[0,L]$, then the statement $x$ ...
- 541
4
votes
Dynamically ending ODE integration in SciPy
The solution is
https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html
From the documentation : ‘RK45’ or ‘RK23’ method for non-stiff problems and ‘Radau’ or ‘BDF’ for ...
- 51
4
votes
Choice of grid generation for FDM discretisation methods
Your question mentions both space and time discretization and the problems that can arise due to different choices of one or the other.
I think that you might be conflating problems that come from the ...
- 9,813
3
votes
Access optimized data structure for representing integer lattice
In essence, you are asking whether you can enumerate the integer lattice sites within your domain from $1$ to $N$ in such a way that accessing the east/west/north/south neighbors of a location $n$ ...
- 53.7k
3
votes
Accepted
Is there an advantage of using a staggered grid over a regular one when combined with high order methods?
Let me formulate my remark as an answer (and make it more precise):
My experience and knowledge is that to use collocated grids with any standard (lower or higher order) methods for this problem, ...
- 1,226
3
votes
Alternative to messy grid node indexing within multiple layers of loops
This is not a good way to do modern programming for many reasons. First of all, as you pointed out, this kind of code is hard to read and maintain. Secondly, this tends to be done in old versions of ...
- 12.2k
2
votes
Quadtree type Grid
Writing C++ code from the ground up for adaptive mesh refinement (as part of a PDE solver) is a relatively complicated endeavor and can easily involve thousands of lines of code for even simple ...
- 1,869
2
votes
Accepted
Converting mass density to point mass approximation on a grid
It seems like you are inventing Barnes-Hut-type algorithm, which is a fundamental accelerated algorithm for n-body simulations. It follows a similar logic: you combine masses on a grid. But, it is ...
- 8,592
2
votes
Grid mapping from Tchebyshev
In the section about adaptive Methods Chapter 16. in "Chebyshev and Fourier Spectral Methods" from John P. Boyd several different coordinate transformations together with their application in ...
- 1,275
2
votes
Finite Difference Grid Spacing and Scaling
Let's assume the following heat transient heat transfer equation in 1D :
$$
\frac{\partial T} {\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}
$$
If we take its finite difference ...
- 1,147
2
votes
Accepted
How to refine the tetrahedron if exist two longest length edge?
The easiest thing is to ensure a consistent (although arbitrary) tie-breaking scheme. If your nodes/vertices indexed, this usually means preferring the split edge with the lowest index of its lowest ...
- 231
2
votes
Mapping derivative information in uniform to non-uniform grid
Use the chain rule to get the derivative on the non-uniform grid, $\frac{dy}{d\zeta}$:
$$
\begin{align}
\frac{dy}{d\zeta} &= \frac{dy}{dx} \frac{dx}{d\zeta}\\
&= \frac{dy}{dx} \cdot 2 \zeta \...
- 343
2
votes
Access optimized data structure for representing integer lattice
You can probably speed things up a little bit by storing the array in 4x4 square subarrays so that each of them fit in cache line (64 bytes = 4x4 32-bit integers). This changes the probability ...
- 131
2
votes
What makes a good computational grid?
The best choice for a numerical grid is the one that will most accurately approximate the solution to your problem (without being too computationally expensive). But beyond that the specific features ...
- 211
2
votes
Grid Independence Study
You've almost certainly got to reduce the timestep to maintain stability due to the CFL condition imposed by your explicit timestepping method choice. That being said, for benchmarking purposes, I'd ...
- 10.9k
2
votes
Accepted
Overlapping 1D grids
Assuming that the arrays are passed already sorted (which is a reasonable assumption since you are starting from two 1D grids), I have a solution which is $\mathcal{O}(n+m)$ where $n$ and $m$ are the ...
- 2,321
2
votes
Accepted
Restriction in (geometric) multigrid for vectors of non-even length
I have found what I was looking for in Wesseling's book: An introduction to multigrid methods. For vectors with an even number of elements, a cell-centered approach is employed where coarser grid ...
- 971
2
votes
Accepted
Grid walk vs. uniform random weights for bounded grid
Not every method that seems reasonable leads to an algorithm that is competitive. In your case, if you want to draw uniform random numbers from $[0,1]^2$, you could use a method that is based on ...
- 53.7k
1
vote
Calculations on discontinous grids
I am not an expert on this question (I used finite elements mostly as a student) but I did use finite differences with a 2D uneven grid recently. My intuition is that, if you use the right ...
- 436
1
vote
can you give me some information of tools for load reblance
I found the ParMetis have what I want and easy to use.
- 323
1
vote
Grid Independence Study
As pointed out in the comments, the CFL condition dictates how big timestep can be. Therefore as we progressively refine in space, we would be required to take smaller time steps if an explicit ...
1
vote
Is it possible to resample grid in such a way so that continuous objects remain continuous?
I think the problem is that you've lost the topology upon the first rasterization:
| 0 | 1 | 1 | 0.5 | 0 |
could be
...
- 253
1
vote
Accepted
Good C, C++ library for efficient grid search / tuples, ideally with bindings to Eigen
I would second the opinion expressed in the context. For that small problem and limited usage, you don't need a library. Generation of a structured grid and retrieving points can be coded up in at ...
- 8,592
1
vote
Three dimensional irregular grid data interpolation to regular grid
For scattered data at points with no structure, try
inverse-distance-weighted-idw-interpolation-with-python.
This combines
scipy's fast K-d_trees
with inverse-distance aka radial kernels:
$\qquad ...
- 912
1
vote
Accepted
Efficient Representation of (spatially sparse) spatial time series
The dataset is huge. So I would like to be more memory-efficient. The main point to consider is the following:
[…] most of the cells will be “unactivated”, i.e most of the elements of the matrix will ...
- 2,022
1
vote
Balancing core load when number of particles in cells vary (PIC on GPU)
You ought to be interested in this preprint in which we discuss exactly the sort of questions you seem to be having: https://arxiv.org/abs/1612.03369
- 53.7k
1
vote
Accepted
Finite Volume Polar Discretization: Lengths
Your cells are not infinitesimally small so it will be a bit more complicated than either formulation you have there. (The ``width'' of your finite volume cell varies nontrivially over the cell, so we ...
- 158
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