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Questions tagged [interpolation]

Interpolation is the process of estimating the values of a function, when the function's values are known only at a particular set of points. Questions on interpolation in one or more dimensions, as well as algorithms for doing so, should have this tag.

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B-Spline basis on a 3D mesh

I need to interpolate some (sparse) data scattered on a 3D manifold mesh. In other words, I have a scattered interpolation problem where the input values are defined for some vertices of the mesh. ...
• 301
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Interpolation constant on triangles

There are quite a few references regarding the estimation for the interpolation error for the piece-wise affine finite elements. I find one particular estimate interesting (and useful in my case), ...
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• 97
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Chebyshev/Lagrange polynomials in spectral methods

I am currently trying to familiarise myself with (Pseudo-)Spectral Methods for solving differential equations. Now, I am struggling to understand some obviously crucial concept of this approach. The ...
• 185
124 views

Interpolating 2D data on a hemisphere in order to have $C^2$ function but no overshoot

I am interpolating a 2D dataset on a hemisphere, and I am currently using scipy.Rbf that I like for its simplicity. I am defining the norm of the interpolator with ...
• 63
1 vote
749 views

If FEM is exact at the nodes, why do first and second-order elements give very different results?

I'm looking at the solution to a structural mechanics problem that is modeled with first-order elements and then as a comparison with second-order elements. It is clear that the first-order elements ...
• 31
280 views

Is 'natural neighbor' interpolation better than linear for unstructured function interpolation?

Natural neighbor interpolation is defined here, it is an intriguing method that uses voronoi diagrams. Notably it is smooth almost everywhere whereas linear interpolation is only piecewise linear. I ...
99 views

Modal representations of nodal tensor product Galerkin elements

Nodal discontinuous Galerkin methods on simplices, like those described in Hesthaven and Warburton, have the nice property that the number of nodes is equal to the minimum number needed to represent a ...
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1 vote
42 views

Integral from function approximations

I have some data which I cannot manage to model and fit with a known function, so let’s say that they are a sample from the unknow function $f(x)$, which look a sort of skewed bell-shaped distribution....
2k views

Fitting a monotonically increasing spline function

I want to fit a monotonically increasing smooth spline function for a dataset Code: ...
• 433
101 views

Interpolation of 1D solution from an original grid to a new grid

I have a solution of a 1D wave on a grid (tangent hyperbolic variation) and now I want to interpolate the obtained solution to a new grid with the same number of points as the previous grid but the ...
• 121
218 views

Which way is the right way to compute the integrals in finite element methods?

Finite element methods involve integrals of functions that are not polynomials, and these integrals must be computed numerically. For example, suppose that $f$ is the right-hand side of a Poisson ...
• 3,680
1 vote
271 views

Finding weighted average of curves

This is related to my previous post here I have a dataset with values of multiple curves. An example plot is shown below. I want to scale the curves (move up/down) so that all curves overlap. The ...
• 433
102 views

Note; No special knowledge of Pykrige is needed to answer the question, as I already mention examples in the question! Hi I would like to use Universal Kriging in my code. For this I have data that ...
491 views

How can I reduce the artifact in "Thin Plate Spline" interpolation?

At the Top "right", there is the 2D-density plot of the recorded data (actual), fewer in number. Recorded data has been sampled a on the 8 arms of a regular octagon. These 8 arms are placed ...
1 vote
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I am using Python 3.7 to write a program that requires me to calculate the root of the Hermite interpolating polynomial, given two points $\epsilon_0$, $\epsilon_1$, the function ($d(\epsilon_0)$,$d(\... • 183 1 vote 3 answers 750 views Bilinear interpolation for large grids I need to make a bilinear interpolation of a function$Y(i,j)$tabulated on a$100\times 100$grid. I tried to do it with the Fortran polin2.f and ... 3 votes 2 answers 120 views How to reconstruct a 2D field from its integral? General question I work on the plane where I have a two-dimensional shape$V$that is cut in a collection of parts$\{V_i\}$that do not overlap$ V_i ~~\text{s.t.}~~ \bigcup_i \overline{V}_i = \...
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I am seeking knowledge from the community. I am solving a transport PDE (conservation of solute mass) using COMSOL. At each Newton-Raphson iteration, I need to update a constant called $Kd$ for some ...