TY - JOUR

T1 - Mesh-independent operator preconditioning for boundary elements on open curves

AU - Hiptmair, Ralf

AU - Jerez-Hanckes, Carlos

AU - Urzúa-Torres, Carolina

N1 - Publisher Copyright:
© 2014 Society for Industrial and Applied Mathematics

PY - 2014

Y1 - 2014

N2 - Boundary value problems for the Poisson equation in the exterior of an open bounded Lipschitz curve C can be recast as first-kind boundary integral equations featuring weakly singular or hypersingular boundary integral operators (BIOs). Based on the recent discovery in [C. Jerez- Hanckes and J. Nédélec, SIAM J. Math. Anal., 44 (2012), pp. 2666-2694] of inverses of these BIOs for C = [ -1, 1], we pursue operator preconditioning of the linear systems of equations arising from Galerkin-Petrov discretization by means of zeroth- and first-order boundary elements. The preconditioners rely on boundary element spaces defined on dual meshes and they can be shown to perform uniformly well independently of the number of degrees of freedom even for families of locally refined meshes.

AB - Boundary value problems for the Poisson equation in the exterior of an open bounded Lipschitz curve C can be recast as first-kind boundary integral equations featuring weakly singular or hypersingular boundary integral operators (BIOs). Based on the recent discovery in [C. Jerez- Hanckes and J. Nédélec, SIAM J. Math. Anal., 44 (2012), pp. 2666-2694] of inverses of these BIOs for C = [ -1, 1], we pursue operator preconditioning of the linear systems of equations arising from Galerkin-Petrov discretization by means of zeroth- and first-order boundary elements. The preconditioners rely on boundary element spaces defined on dual meshes and they can be shown to perform uniformly well independently of the number of degrees of freedom even for families of locally refined meshes.

KW - Boundary integral operators

KW - Fracture problems

KW - Operator (Calderón) preconditioning

KW - Screen problems

UR - http://www.scopus.com/inward/record.url?scp=84911396099&partnerID=8YFLogxK

U2 - 10.1137/130947040

DO - 10.1137/130947040

M3 - Article

AN - SCOPUS:84911396099

VL - 52

SP - 2295

EP - 2314

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 5

ER -