- Title
- The development of efficient algorithms for large-scale finite element limit analysis
- Creator
- Podlich, Nathan
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2018
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Finite element limit analysis is a useful numerical method for stability assessment of a wide range of geotechnical and structural applications yielding lower and upper bound estimates on the ultimate loads which can be exerted on the structure. The most advanced formulations of numerical limit analysis are often cast as a conic optimisation problem, which is then solved very efficiently by specialised interior point methods. However, as the problems become larger, especially in three dimensions the computational demands in terms of both storage and time increase significantly. This Thesis details the development of efficient methods for the solution of linear systems and presolve routines within an interior point framework for conic programs. Therefore, these methods all aim to reduce the computational time required to solve the finite element limit analysis problems. The solution of a linear system comprises the majority of the computational requirements and is thus the primary concern of this Thesis. A range of preconditioners for Krylov subspace iterative solvers are considered, as well as more conventional direct solvers and their parallelisation. The presolve routines seek to reduce the size of the optimisation problem to be solved and avoid likely numerical difficulties. Preconditioners for Krylov subspace iterative solvers are the primary determinant for the success of an iterative solver-based approach. A range of preconditioners are developed for both positive-definite and symmetric indefinite linear systems in attempt to avoid the significant runtime and storage requirements associated with the direct solvers. The best performing methods are tested against state-of-the-art implementations using direct solvers on a set of test problems but are found to be uncompetitive in their runtime performance and their robustness. The focus is then switched to the parallelisation of a direct solver on modern hardware including massively parallel GPUs to reduce the computation time with significant gains achieved. In addition to exploiting the full power of parallel processing, the Thesis develops and describes presolve routines which target effective treatment of fixed and free variables. The fixed variables cannot be immediately substituted out of the problem because they are associated with other variables through a conic constraint, but may still be exploited by careful manipulation of the linear system. The free variables can sometimes be substituted out of the problem, however, avoiding the numerical difficulties they often present. This is achieved without increasing the size of the linear system to be solved, although it may require the ability to handle dense columns. Finally, an approach for solving a linear system with dense columns is detailed similar to that of exploiting the fixed variables.
- Subject
- finite element limit analysis; interior point method; Cholesky factorisation; linear systems
- Identifier
- http://hdl.handle.net/1959.13/1386306
- Identifier
- uon:32396
- Rights
- Copyright 2018 Nathan Podlich
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 3 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 57 KB | Adobe Acrobat PDF | View Details Download |