Applications of the Digital-Discrete Method in Smooth-Continuous Data Reconstruction
For researchers in data reconstruction, this method offers an alternative to classical approaches like splines or finite elements, but the results are preliminary and incremental.
The paper introduces a digital-discrete method for smooth-continuous data reconstruction that avoids domain decomposition, demonstrating its flexibility on water well logs and harmonic functions on 2D manifolds with six algorithms.
This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition according to guiding (or sample) points. Then uses Splines (for polynomial) or finite elements method (for PDE) to fit the data. Our method is based on the gradually varied function that does not assume the property of the linearly separable among guiding points, i.e. no domain decomposition methods are needed. We also demonstrate the flexibility of the new method and the potential to solve variety of problems. The examples include some real data from water well logs and harmonic functions on closed 2D manifolds. This paper presented the results from six different algorithms. This method can be easily extended to higher multi-dimensions.