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# Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method

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School of Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
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Authors to whom correspondence should be addressed.
Water 2020, 12(12), 3580; https://doi.org/10.3390/w12123580
Received: 2 December 2020 / Revised: 17 December 2020 / Accepted: 17 December 2020 / Published: 20 December 2020
(This article belongs to the Special Issue Meshless Methods for Water Dynamics and Complex Flows)
This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to validate the proposed approach. Emphasis is placed on the two-dimensional boundary detection problem in which the nonlinearity is solved using the fictitious time integration method. Results demonstrate that approximations with high accuracy are acquired in which the boundary data on the absent boundary may be efficiently recovered even when inaccessible partial data are provided. View Full-Text
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MDPI and ACS Style

Ku, C.-Y.; Hong, L.-D.; Liu, C.-Y. Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method. Water 2020, 12, 3580. https://doi.org/10.3390/w12123580

AMA Style

Ku C-Y, Hong L-D, Liu C-Y. Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method. Water. 2020; 12(12):3580. https://doi.org/10.3390/w12123580

Chicago/Turabian Style

Ku, Cheng-Yu, Li-Dan Hong, and Chih-Yu Liu. 2020. "Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method" Water 12, no. 12: 3580. https://doi.org/10.3390/w12123580

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