MACSI at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar

**Date Friday, 26 ^{th} April 2019, Room A2-002 at 4 p.m. **

**Speaker:** Prof. Mauro Giudici (Department of Earth Sciences "Ardito Desio", Università degli Studi di Milano, Italy).

**Title: **Inverse problems in groundwater hydrology: basic properties and examples of solution methods.

**Abstract: **The basic inverse problem of groundwater hydrology under stationary flow conditions, i.e., finding hydraulic conductivity or transmissivity from potential (hydraulic head) and source/sink terms, corresponds to the identification of the leading coefficient of an elliptic equation. Conditions to obtain a unique solution have been studied since a long time. Moreover, stability issues related to the lack of continuity of the mapping from hydraulic head to hydraulic gradient are well known and can be further examined through spectral analysis of the balance equation. In the discrete case, e.g., for finite differences or finite volume discretization, the stability issue should be considered more carefully and should not be confused with that of well-conditioning, as shown by simple paradigmatic examples.

The above mentioned topics can be examined also with numerical tests corresponding to different strategies. With a first set of tests, different direct methods of solution of the inverse problem are compared, by applying them in a "tomographic" framework, i.e., when data from multiple flow situations are available. A second set of tests shows the relevance of joining inverse modeling to obtain the long-wavelength variability of the conductivity field with geostatistical modeling (in the specific case, multiple point geostatistics) to reproduce the short-wavelength variability.

**Further Information**: If you have any questions regarding this seminar, please direct them to Romina Gaburro (061 2131930, email romina.gaburro@ul.ie or Clifford Nolan (061 202766), clifford.nolan@ul.ie).

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.