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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1answer
6k views

How does Matlab's "interp2" compute bicubic interpolation?

Computational Science people: The title is the question: exactly how does Matlab's "interp2" command (with the "cubic" option) perform bicubic interpolation? I tried the Mathworks documentation ...
6
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2answers
237 views

Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0

I have some function of $R^2$, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0. $$ f(x,y) = \Re\left[\int_0^{x + iy}...
4
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1answer
360 views

Surface interpolation from two lines

Sorry if this is a basic problem but I don't know where to start looking (mainly because being an outsider I don't know the terms and nomenclature). Imagine two perpendicular lines ("profiles") in a "...
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1answer
38 views

Adding data with different abscissas

This question may be better suited for an Astronomy Stack Exchange site, but I figured I'd ask here. Say I have measurements of something as a function of radius for a number of objects. Here's an ...
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0answers
160 views

How do I implement thin plate splines with barriers?

I want to implement thin spline interpolation of scattered elevation data $ \{z_i(x_i,y_i)\}_{i=1..n} $ in C++. This seems fairly simple using Radial Basis Functions: $$ z(x,y) = p(x,y) + \sum_i l_i\...
5
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2answers
9k views

SciPy interpolation with Univariate Splines

I have coded a routine for interpolation with B-splines, only to discover later that this functionality is already included in Python's SciPy. However, I do not understand one parameter in the SciPy ...
7
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2answers
3k views

Intermediate values (interpolation) after Runge-Kutta calculation

I have a numerical ODE simulation that I computed at fixed time step $h$ using a 4-th order Runge-Kutta method (RK4), producing a series of results $(x_1,y_1), (x_2,...
7
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5answers
10k views

Interpolate 2D data

I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an ...
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0answers
30 views

Combining trend estimation and constrained Marquart fit

This title certainly needs some clarification: I need to compute parameters $a_i$ for a helper function $f(\vec{a};k)$ (for grid interpolation) which is fitted to a number of values $y_k$ which are ...
3
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2answers
1k views

How to properly use polynomial projection to get values at visualization nodes?

I am trying to implementing a nodal discontinuous Galerkin spectral element method for linear and non-linear systems of equations. The solution at each time step is given at ...
0
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1answer
51 views

Clarification on interpolation equalities given by Briggs

Briggs, "A Multigrid Tutorial" (pg. 35) has the following expressed as 2-D interpolation: \begin{align*} v^h_{2i,2j} &= v_{i,j}^{2h}\\ v^h_{2i+1,2j} &= 0.5\cdot(v_{i,j}^{2h} + v_{i+1,j}^{2h})\\...
4
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1answer
957 views

Prolongation/Restriction Operator in Multigrid

In Multigrid, using Poisson's equation, does the equality below always hold regardless of what type of boundary conditions you use? $$ R= c\cdot I^T, \text{ for some constant }c $$ where $R$ and $I$ ...
2
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1answer
75 views

Integrating from tabular data, in particular steam tables

I'd like to be able to view in graph form the volume and pressure of steam produced from heating water in a sealed vessel, starting from room temperature water. Important variables, such as the ...
2
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0answers
50 views

Propogated Error in Mesh Interpolation

I am working with a code that solves diffusion/reaction equations on a 2D unstructured mesh. Due to the stiffness of some of the processes, I start with time steps near 1e-13, and end with a final ...
6
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1answer
1k views

restriction and interpolation in multigrid method

I need detailed explanation of the formula below A2=I1*A1*I2 I suppose this formula computes matrix A2 on a coarse grid and here A1 is original matrix on fine ...
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4answers
2k views

When we use Bernstein polynomials in application

When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple ...
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1answer
555 views

ENO/WENO vs monotone Hermite interpolation

I have see the method PCHIP in matlab that implements the monotone Hermite interpolation method which was originally proposed by Carlson in 1980s. It seem to accomplish the goal of preventing the ...
6
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1answer
210 views

What is the most efficient approach to interpolate values between two FEM meshes in 2D?

I am looking for efficient algorithm to interpolate values from one unstructured 2D mesh grid to another. Both grids are constructed using the same type of elements (triangles or quadrilaterals). Both ...
6
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1answer
230 views

interpolation combined with methods of characteristics can cause oscillations for the transport equation?

I would like to know about the effect of using a higher order interpolator for the methods of characteristics. I am solving $$u_t+a(x,t)u_x=0$$ with some nonsmooth initial data $u_0(x)$ by the method ...
6
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2answers
6k views

Piecewise polynomial interpolation: Hermite vs Lagrange

I am a bit confused of the qualitative behavior of the two methods. Consider quadratic case, start by having points $x_i$, where I know the value and points $y_j$, where the values to be found. If I ...
2
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0answers
107 views

Resampling of values between body fitted and cartesian grids

Assuming there exist two 2D grids on the same domain, one of them is a cartesian one while the other is curvilinear (body fitted regular grid, with curved coordinate lines). I am looking for a way to ...
5
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2answers
669 views

Interpolation schemes to move data between cells and nodes

I work on non-graded quadtree grids where the entire grid is a hierarchy of cells specified using a quadtree data structure, where, in general, there is no constraint regarding the relative size of ...
2
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2answers
931 views

error of linear interpolation

I have two points $x_1, x_2$ between which I would like to have a linear interpolation $P_1$. Those two points are just points where I know the value of the underlying function $f$. I know that the ...
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4answers
6k views

Efficient interpolation method for unstructured grids?

I would like to know a good method for interpolating data between two unstructured grids, where one grid is a coarser version of the other. Efficiency is very important to me since I'm solving a ...
11
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2answers
2k views

How to interpolate multipoint data to the cell centres of an unstructured mesh?

I have sets of multipoint field data, each point data set relates to a single cell of an unstructured mesh. The goal is to interpolate the data to the cell centre, directly or indirectly, in the most ...
8
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4answers
4k views

High Order derivatives of splines using SciPy

I have created a spline to fit my data in python using: spline=scipy.interpolate.UnivariateSpline(energy, fpp, k=4) The equation I want to use involves a ...
9
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1answer
1k views

What is the most accurate interpolation method for a 3D-flowfield on a structured grid?

I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and ...

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