Abstract
This chapter develops the application of PGD methods for linear elasticity problems. The only difficulty relies in the vectorial character of the unknown, the displacement field.
Classical mathematics concentrated on linear equations for a sound pragmatic reason: it could not solve anything else.
—Ian Stewart
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Notes
- 1.
Note that we employ the word converged since the PGD algorithm implies the solution of a non-linear problem by an alternating directions strategy . Keep in mind that the proposed linearization for the global problem is indeed explicit, so there is no need to converge in a Newton-Raphson sense.
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Cueto, E., González, D., Alfaro, I. (2016). PGD for Non-linear Problems. In: Proper Generalized Decompositions. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29994-5_4
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DOI: https://doi.org/10.1007/978-3-319-29994-5_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29993-8
Online ISBN: 978-3-319-29994-5
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