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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
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A practical adaptive moving-mesh algorithm for solving unconfined seepage problem with Galerkin finite element

Qianwei Dai1,2, Yi Lei1,2, Bin Zhang3,4

  • 1School of Geosciences and Info-Physics, Central South University, Changsha, 410083, P.R. China.

Scientific Reports
|May 8, 2019
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Summary

Accurately determining the free surface in complex dam seepage models is challenging. This study introduces an adaptive moving-mesh and finite element method (FEM) approach that significantly improves efficiency and precision in free-surface searching.

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Area of Science:

  • Geotechnical Engineering
  • Computational Fluid Dynamics
  • Hydrology

Background:

  • Unconfined seepage in dams presents challenges in accurately defining the free surface.
  • Model complexity, including intricate geometry and varied permeability, complicates seepage analysis.

Purpose of the Study:

  • To present a practical methodology for efficiently and precisely solving unconfined seepage problems.
  • To address the accurate determination of the free surface in complex seepage models.

Main Methods:

  • Combines the adaptive moving-mesh algorithm with the Galerkin finite element method (FEM).
  • Incorporates improvement terms like remainder factor, step-size parameter, and termination condition for convergence.
  • Analyzes the relationship between the exit point location and grid fineness.

Main Results:

  • The proposed methodology achieves high efficiency and precision in free-surface determination.
  • Simulation and grid refinement converge effectively within a specified error tolerance.
  • Demonstrates significant improvements in free-surface searching accuracy and efficiency compared to other numerical methods.

Conclusions:

  • The adaptive moving-mesh and FEM approach offers a practical solution for complex unconfined seepage problems.
  • The method enhances accuracy and efficiency, even with complex geometries and permeability variations.
  • Provides a robust tool for geotechnical and hydrological engineering applications.