A Nyström scheme with rational quadrature applied to edge crack problems | Zendy

Englund J. | Zendy

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A Nyström scheme with rational quadrature applied to edge crack problems

Author(s) -

Englund J.

Publication year - 2007

Publication title -

communications in numerical methods in engineering

Language(s) - English

Resource type - Journals

eISSN - 1099-0887

pISSN - 1069-8299

DOI - 10.1002/cnm.937

Subject(s) - preconditioner , quadrature (astronomy) , nyström method , discretization , mathematics , solver , computation , mathematical analysis , iterative method , algorithm , integral equation , mathematical optimization , physics , optics

The effects of introducing rational quadrature into a recently developed algorithm for the computation of the stress field in edge‐cracked specimens are studied. The algorithm is based on an integral equation of the second kind which is solved using a Nyström method. Rational quadrature can handle the presence of corners and triple‐junctions in a more accurate manner than can polynomial quadrature. A preconditioner is also included in the scheme. The rational quadrature together with the preconditioner results in a scheme that reduces the number of discretization points needed for a certain accuracy by up to 70% and the number of iterations needed by an iterative solver by up to 50%, compared to a scheme using only polynomial quadrature. For validation, several setups with a single edge crack are studied. Larger setups containing up to 1500 edge cracks are also investigated. Copyright © 2006 John Wiley & Sons, Ltd.

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