Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science
Numerical Analysis
2025-10-28 v1 Numerical Analysis
Abstract
This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used to model boundary values while the inner point data is used for modeling a load vector with the goal to generate a smooth surface. The construction of boundary data is an ill-posed problem, for which a special regularization approach is suggested. The method is designed for surface construction problems with a very limited amount of measured data. In the paper we apply the method by using empirical data of soil thickness and geological maps indicating exposed bedrock regions.
Cite
@article{arxiv.2510.23195,
title = {Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science},
author = {Samson Seifu Bekele and Maregnesh Mechal Wolde and Claus Führer and Nils-Otto Kitterød and Anne Kværnø},
journal= {arXiv preprint arXiv:2510.23195},
year = {2025}
}