Parallel Algorithm for Natural Neighbour Interpolation

2nd Ural Workshop on Parallel, Distributed, and Cloud Computing for Young Scientists Yekaterinburg, Russia, October 6, 2016

Parallel Algorithm for Natural Neighbor Interpolation (slide 1 / 19)



Parallel Algorithm for Natural Neighbor Interpolation

Alexander TsidaevBulashevich Institute of Geophysics

Ural Federal University (IRIT-RTF)Yekaterinburg




Initial Data

Seismic data is principally two-dimensional.

We need to construct 3D models.

Typical seismic profile (recalculated to density values):

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Interpolation of the 2D data

Interpolation is the key step for initial model construction.This model contains 801 layers.



Interpolation methods



Natural Neighbor Interpolation Method

based on image by Markluffel, distributed under CC BY-SA 3.0

is the measured (initial) value in point

is ratio of ”stolen” area



Voronoi Diagrams

Voronoi diagram for 13 points

The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other.



Iterative (incremental) algorithm for Voronoi

Based on incremental methodby Green, Sibson (1978)




Searching intersection points forall polygons.

could be calculated on these steps for all the affected points.





























When we meet some edge for the second time, the algorithm reaches the end.







Resulting new polygion is constructed



ParallelizationIt can be noted that:

1. Algorithm is non-obstructive: none of the input data values are changed during calculation. This is the feature of any interpolation algorithm, that the interpolated function remains the initial values in the points of initial set.

2. Value in any inserted point depends only on values of the initialset.

So the calculations for any number of interpolated points can be performed in any order. This makes possible to implement the simple parallelization case of multiple independent threads. One thread for each interpolation point.



Efficiency of Parallel Version

Test calculations were performed on the URAN supercomputer (Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg).

Initial set contained 644 points, interpolation grid was a square of 1024x1024 points.

Two parallelization platforms were used – OpenMP and CUDA.



Thank you for your attention

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Parallel Algorithm for Natural Neighbour Interpolation