Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science
(2025) In arXiv.org- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b5804093-ca9e-47cf-be61-3a7e0ec13ae8
- author
- Seifu Bekele, Samson ; Mechal Wolde, Maregnesh ; Führer, Claus LU ; Kitterød, Nils-Otto and Anne Kværnø, Anne
- organization
- publishing date
- 2025-10-27
- type
- Contribution to journal
- publication status
- published
- subject
- in
- arXiv.org
- publisher
- Cornell University Library
- ISSN
- 2331-8422
- project
- Numerical Analysis and Scientific Computing
- language
- English
- LU publication?
- yes
- id
- b5804093-ca9e-47cf-be61-3a7e0ec13ae8
- alternative location
- https://doi.org/10.48550/arXiv.2510.23195
- date added to LUP
- 2025-11-08 12:29:48
- date last changed
- 2026-02-17 10:28:02
@article{b5804093-ca9e-47cf-be61-3a7e0ec13ae8,
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.<br/> 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. <br/><br/>}},
author = {{Seifu Bekele, Samson and Mechal Wolde, Maregnesh and Führer, Claus and Kitterød, Nils-Otto and Anne Kværnø, Anne}},
issn = {{2331-8422}},
language = {{eng}},
month = {{10}},
publisher = {{Cornell University Library}},
series = {{arXiv.org}},
title = {{Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science}},
url = {{https://doi.org/10.48550/arXiv.2510.23195}},
year = {{2025}},
}