Techniques to accelerate BEM computation to provide virtual reality update of stress solutions

Trevelyan, James; Scales, Derek

doi:10.1016/j.enganabound.2007.04.004

Cited by 3 publications

(5 citation statements)

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“…For clarity this will be referred to simply as LU preconditioning throughout this paper. If it is assumed that each geometric update is small, {x i−1 } can be used to reduce the solution time by providing a good first approximation of {x i } [12].…”

Section: Iterative Methodsmentioning

confidence: 99%

“…Both diagonal and complete approximate LU a [12] preconditioning have been applied to the GMRES, BiCGSTAB and TFQMR algorithms. The applied LU preconditioner is the complete LU decomposition of [A 0 ], generated during the initial analysis.…”

Section: Iterative Methodsmentioning

confidence: 99%

“…The mesh updating procedure is designed to minimise the number of elements affected when the model geometry is updated. This minimises the number of integrals, contained in the system matrix, that need to be recalculated before re-analysis and improves the convergence rate of a preconditioned iterative solver [12]. If the same total number of elements is maintained then the preconditioning matrix used by the solver can be re-used.…”

Section: Re-meshing a Geometric Perturbationmentioning

confidence: 99%

“…However, the LU preconditioner must be recomputed sparingly (if at all), as it is expensive to compute, and only after a minimum of n/40 updates have been applied to maintain the efficiency of the process. Alternatively an new LU preconditioner can be generated by a separate process in a new thread [12], thereby not detracting from the re-solution time.…”

Section: Solution Of the System For A Fixed Accuracymentioning

confidence: 99%

“…Reducing the number of updated elements gives rise to a reduction in both the time to re-integrate and re-assemble the linear system of equations generated by the BEM and the time required to solve these equations [12]. Michler [13] uses techniques based on radial basis functions to locally distort a aircraft mesh based on geometric changes.…”

Section: Introductionmentioning

confidence: 99%

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Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis

Foster

Mohamed

Trevelyan

et al. 2012

Engineering Analysis with Boundary Elements

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(2012) 'Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis.', Engineering analysis with boundary elements., 36 (9). pp. 1331-1343. Further information on publisher's website:http://dx.doi.org/10.1016/j.enganabound.2012.02.020Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Engineering Analysis with Boundary Elements. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version was subsequently published in Engineering Analysis with Boundary Elements, 39, 9, September 2012, 10.1016/j.enganabound.2012.02.020. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractStructural design of mechanical components is an iterative process that involves multiple stress analysis runs; this can be time consuming and expensive. It is becoming increasingly possible to make significant improvements in the efficiency of this process by increasing the level of interactivity. One approach is through real-time re-analysis of models with continuously updating geometry. A key part of such a strategy is the ability to accommodate changes in geometry with minimal perturbation to an existing mesh. This work introduces a new re-meshing algorithm that can generate and update a boundary element mesh in real-time as a series of small changes are sequentially applied to the associated model. The algorithm is designed to make minimal updates to the mesh between each step whilst preserving a suitable mesh quality that retains accuracy in the stress results. This significantly reduces the number of terms that need to be updated in the system matrix, thereby reducing the time required to carry out a re-analysis of the model. A range of solvers are assessed to find the most efficient and robust method of re-solving the system. The GMRES algorithm, using complete approximate LU preconditioning, is found to provide the fastest convergence rate.

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Section: Iterative Methodsmentioning

confidence: 99%

Section: Iterative Methodsmentioning

confidence: 99%

Section: Re-meshing a Geometric Perturbationmentioning

confidence: 99%

Section: Solution Of the System For A Fixed Accuracymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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