# Tag Info

### 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 ...
• 3,005
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, ...
• 1,264

### 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
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

### 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 ...
• 10.4k
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 ...
• 2,197

### 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 $n$ ...
• 55.9k

### 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 ...
• 12.4k
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 ...
• 8,702

### 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 ...
• 1,285

### 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 ...
• 1,157

### 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

### 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
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 ...
• 241

### 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

### 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
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 ...
• 2,821
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 ...
• 55.9k
1 vote
Accepted

### Creating nonuniform grids for FDM with multiple points of concentration

Let $\xi_1(𝑖)$ be a mapping providing refined resolution at $𝑖_1$ and $\xi_2(𝑖)$ be a mapping providing refined resolution at $𝑖_2$. Then $\xi_3(𝑖)=\xi_1 \xi_2/𝑖$ should be the mapping providing ...
• 2,595
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 ...
• 8,702
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 ...
• 932
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 ...
• 2,032
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
• 55.9k
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
1 vote

### 3-dimensional plotting with nonuniform grids

Your data is already in the right shape, then you don't need to create a meshgrid. See the code below ...
• 8,582
1 vote
Accepted

### Contour plot interpolation recommendation

If your data are regularly spaced, you do not need an interpolation procedure, you can directly plot a contour through a contour or a ...
• 629

Only top scored, non community-wiki answers of a minimum length are eligible