NDLI: Solving 3D boundary element problems using constrained iterative approach

Content Provider	Springer Nature Link
Author	Maerten, Frantz Maerten, Laurent Cooke, Michele
Copyright Year	2009
Abstract	Some major challenges for geophysicists and structural geologists using three-dimensional boundary element method codes (3D-BEM) are: (1) reducing the amount of memory required to solve large and dense systems and (2) incorporation of inequality constraints such as traction inequality constraints (TIC) and displacement inequality constraints (DIC). The latter serves two purposes. First, for example, inequality constraints can be used to simulate frictional slip (using TIC). Second, these constraints can prevent element interpenetration while allowing opening mode (using DIC). We have developed a method that simultaneously incorporates both types of functionality of the inequality constraints. We show that the use of an appropriate iterative solver not only avoids the allocation of significant memory for solving the system (allowing very large model computation and simplifying parallelization on multi-core processors), but also admits interesting features such as natural incorporation of TICs and DICs. Compared to other techniques of contact management (e.g., Lagrange multipliers, penalty method, or complementarity problem), this new simple methodology, which does not use any incremental trial-and-error procedures, brings more flexibility, while making the system more stable and less subject to round-off errors without any computational overhead. We provide validations and comparisons of the inequality constraints implementation using 2D analytical and numerical solutions.
Starting Page	551
Ending Page	564
Page Count	14
File Format	PDF
ISSN	14200597
Journal	Computational Geosciences
Volume Number	14
Issue Number	4
e-ISSN	15731499
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-10-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	3D-BEM Iterative solver Inequality constraints Friction Mathematical Modeling and Industrial Mathematics Soil Science & Conservation Hydrogeology Geotechnical Engineering
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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