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Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science

Seifu Bekele, Samson ; Mechal Wolde, Maregnesh ; Führer, Claus LU ; Kitterød, Nils-Otto and Anne Kværnø, Anne (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:
author
; ; ; and
organization
publishing date
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}},
}