6 votes

What are systematic ways of approximating a non-smooth (non-continuously differentiable) system dynamic to be n-smooth?

Two systematic ways of smoothing a function $h$ would be: 1. Join the piecewise smooth parts of your function using Hermite interpolation so that the derivatives are matched to your satisfaction. 2. ...
6 votes

How to "smoothen" (not just refine) a 2D/3D polygonal mesh

To complement the two answers from Daniel Shapero and Nicoguaro: Basically, there are two ways of smoothing a mesh, subdivision (generate new vertices) and smoothing (move the points in such a way ...
  • 2,215
5 votes

How to "smoothen" (not just refine) a 2D/3D polygonal mesh

As mentioned in the answer by @DanielShapero, you can follow an approach based on local approximations of the curvature for your nodes. In the post he suggest, there is an article by Desbrun. I would ...
  • 8,129
4 votes

How to "smoothen" (not just refine) a 2D/3D polygonal mesh

For just mesh smoothing, you can start by looking at Laplacian smoothing and some of the references therein. The idea is to update the position of every vertex in the interior of the mesh by replacing ...
4 votes
Accepted

what is the meaning of mesh smoothing steps in Gmsh?

Meshing algorithms can place the vertices of triangles and tetrahedra in a wide variety of ways, but they are us usually essentially constructive (i.e new vertices are introduced, existing vertices ...
  • 2,199
3 votes

How the number of pre-smoothing and post-smoothing steps affect the asymtotic convergence rate of geometrical Multigrid?

Separately, but it does depend. Not very strongly, however: A very large number of pre- and post-smoothing steps only improves the convergence rate a little bit over a large number of steps. The ...
3 votes
Accepted

Smoothness regularisation of a 2D field on a triangular mesh?

In microwave imaging, a great chunk of literature is devoted to regularization and its effect on the solution process and inversion results. One of the common methods for microwave imaging is the ...
  • 8,461
3 votes

How to "smoothen" (not just refine) a 2D/3D polygonal mesh

Surprisingly, Lloyd smoothing hasn't come up here yet. Check out Du, Qiang; Faber, Vance; Gunzburger, Max (1999), "Centroidal Voronoi tessellations: applications and algorithms", SIAM Review, 41 (4):...
3 votes

Having smoother contour plots in MATLAB

Is the white part NaNs? If so, then you will need to use some sort of extrapolation to smooth that region. The function inpaint_nans may be appropriate (it smoothly fills in NaN regions, essentially ...
  • 336
2 votes

Having smoother contour plots in MATLAB

You can regard your original matrix as an image (i.e., a real-valued function $I = I(x, y)$), then you can apply a Gaussian filter (convolve $I$ with a Gaussian kernel), and finally you can get the ...
2 votes

Value of density when there are no or very few neighbours in SPH simulation

Yes. You need to choose the radius $h$ large enough that for each particle, there is always a significant number of other particles within the first particle's radius.
2 votes
Accepted

What penalty function produces optimization-based Gaussian smoothing?

The least squares optimization problem in your question has a penalty term that only penalizes 1st derivatives. However, for a Gaussian kernel, the corresponding penalty term would have to penalize ...
1 vote

Prevent single node spikes in a FEM-simulation (using continuous Galerkin)

I believe these issues arise because you are solving the transient form of the heat equation which, being parabolic, can lead to some instability for continuous galerkin method. There are ways to ...
  • 1,137
1 vote
Accepted

Scaling factor of the inverse Fourier Transform (for convolution purposes)

You have to normalize by the number of elements in the FFT. That is if the size of your matrix is $(NxM)$ you must normalize your FFT by $(NxM)$. You can check this is valid by looking at the energy ...
  • 354
1 vote

How to connect two fitted B-spline curve?

Fitting together B-splines with a given continuity is a hard problem. This was actually the motivation behind developing a generalization of NURBS called T-splines. There are many articles on T-...
  • 373

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