On the solution of some inverse problems in infiltration

Denis Constales; Jozef Kačur

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 307-322
  • ISSN: 0862-7959

Abstract

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In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA. Several numerical experiments are included.

How to cite

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Constales, Denis, and Kačur, Jozef. "On the solution of some inverse problems in infiltration." Mathematica Bohemica 126.2 (2001): 307-322. <http://eudml.org/doc/248849>.

@article{Constales2001,
abstract = {In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA. Several numerical experiments are included.},
author = {Constales, Denis, Kačur, Jozef},
journal = {Mathematica Bohemica},
keywords = {porous media equation; inverse problems; Richard’s equation; soil parameters for unsaturated porous media; automatic differentiation; numerical experiments; porous media equation; soil parameters for unsaturated porous media; Richard's equation; automatic differentiation; numerical experiments},
language = {eng},
number = {2},
pages = {307-322},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the solution of some inverse problems in infiltration},
url = {http://eudml.org/doc/248849},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Constales, Denis
AU - Kačur, Jozef
TI - On the solution of some inverse problems in infiltration
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 307
EP - 322
AB - In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA. Several numerical experiments are included.
LA - eng
KW - porous media equation; inverse problems; Richard’s equation; soil parameters for unsaturated porous media; automatic differentiation; numerical experiments; porous media equation; soil parameters for unsaturated porous media; Richard's equation; automatic differentiation; numerical experiments
UR - http://eudml.org/doc/248849
ER -

References

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  10. Cauchy problems and boundary-value problems for equations of type of infiltration, Izv. AN SSSR Ser. Mat. 5 (1958), 667–704. (Russian) (1958) 
  11. 10.1137/0904010, SIAM J. Sci. Stat. Comput. 4 (1983), 136–148. (1983) Zbl0518.65051MR0689694DOI10.1137/0904010
  12. 10.1029/90WR02776, Water Resources Research 27 (1991), 1361–1373. (1991) DOI10.1029/90WR02776
  13. 10.1007/BF00250838, Arch. Rational Mech. Anal. 78 (1982), 173–198. (1982) MR0648943DOI10.1007/BF00250838
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