Bitterlich S, Knabner P (2004)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2004
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis
Book Volume: 12
Pages Range: 361-378
Journal Issue: 4
DOI: 10.1080/10682760310001597482
This article deals with the determination of nonlinear coefficient functions in partial differential equations in the field of soil science. We consider two examples to illustrate the numerical determination of nonlinear coefficient functions. In detail, these are the determination of the sorption characteristic of a chemical and the determination of the unsaturated hydraulic properties of a porous medium from measurements obtained from suitable column experiments. This inverse problem is treated by minimizing a least square functional. To cope with the ill-posedness, we apply a parametrization of the unknown nonlinear coefficient function, which is defined by an appropriate interpolation. The parametrization does not use a priori assumptions, which are not justified by physical properties. This kind of parametrization permits a hierarchical approach in the number of the degrees of freedom used. According to the hierarchical structure, we integrate the determination of the coefficient functions into a multi-level procedure. The investigation of the stability of the parametrization is based on the singular values of the sensitivity matrix.
APA:
Bitterlich, S., & Knabner, P. (2004). Numerical methods for the determination of material properties in soil science. Inverse Problems in Science and Engineering, 12(4), 361-378. https://doi.org/10.1080/10682760310001597482
MLA:
Bitterlich, Sandro, and Peter Knabner. "Numerical methods for the determination of material properties in soil science." Inverse Problems in Science and Engineering 12.4 (2004): 361-378.
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