Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912672323207168 |
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| author | Bekele, Samson Seifu Wolde, Maregnesh Mechal Führer, Claus Kitterød, Nils-Otto Kværnø, Anne |
| author_facet | Bekele, Samson Seifu Wolde, Maregnesh Mechal Führer, Claus Kitterød, Nils-Otto Kværnø, Anne |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science Bekele, Samson Seifu Wolde, Maregnesh Mechal Führer, Claus Kitterød, Nils-Otto Kværnø, Anne Numerical Analysis 65D17, 65N21, 65N22, 86-10 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. |
| title | Modeling a Smooth Surface by a Constrained Biharmonic Equation with Application in Soil Science |
| topic | Numerical Analysis 65D17, 65N21, 65N22, 86-10 |
| url | https://arxiv.org/abs/2510.23195 |