English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Helmholtz decompositions of elastic fields is a common approach for thesolution of Navier scattering problems. Used in the context of BoundaryIntegral Equations (BIE), this approach affords solutions of Navier problemsvia the simpler Helmholtz boundary integral operators (BIOs). Approximations ofHelmholtz Dirichlet-to-Neumann (DtN) can be employed within a regularizingcombined field strategy to deliver BIE formulations of the second kind for thesolution of Navier scattering problems in two dimensions with Dirichletboundary conditions, at least in the case of smooth boundaries. Unlike the caseof scattering and transmission Helmholtz problems, the approximations of theDtN maps we use in the Helmholtz decomposition BIE in the Navier case requireincorporation of lower order terms in their pseudodifferential asymptoticexpansions. The presence of these lower order terms in the Navier regularizedBIE formulations complicates the stability analysis of their Nystr\"omdiscretizations in the framework of global trigonometric interpolation and theKussmaul-Martensen kernel singularity splitting strategy. The main difficultystems from compositions of pseudodifferential operators of opposite orders,whose Nystr\"om discretization must be performed with care viapseudodifferential expansions beyond the principal symbol. The error analysisis significantly simpler in the case of arclength boundary parametrizations andconsiderably more involved in the case of general smooth parametrizations whichare typically encountered in the description of one dimensional closed curves.

Stability estimates of Nystr\"om discretizations of Helmholtz  decomposition boundary integral equation formulations for the solution of  Navier scattering problems in two dimensions with Dirichlet boundary  conditions