Browsing by Author "Hiptmair, Ralf"

Now showing 1 - 5 of 5
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    Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks
    (2018) Hiptmair, Ralf; Jerez-Hanckes, C.; Urzua-Torres, C.
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    Convergence of the natural HP-BEM for the electric field integral equation on polyhedral surfaces
    (2009) Bespalov, Alexei; Heuer, Norbert; Hiptmair, Ralf
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    Extension by zero in discrete trace spaces : Inverse estimates
    (2015) Hiptmair, Ralf; Jerez Hanckes, Carlos F.; Mao, Shipeng
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    MESH-INDEPENDENT OPERATOR PRECONDITIONING FOR BOUNDARY ELEMENTS ON OPEN CURVES
    (2014) Hiptmair, Ralf; Jerez-Hanckes, Carlos; Urzua-Torres, Carolina
    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. Nedelec, 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.
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    Sparse tensor edge elements
    (2013) Hiptmair, Ralf; Jerez-Hanckes, Carlos; Schwab, Christoph
    We consider the tensorized operator for the Maxwell cavity source problem in frequency domain. Such formulations occur when computing statistical moments of the fields under a stochastic volume excitation. We establish a discrete inf-sup condition for its Ritz-Galerkin discretization on sparse tensor product edge element spaces built on nested sequences of meshes. Our main tool is a generalization of the edge element Fortin projector to a tensor product setting. The techniques extend to the surface boundary edge element discretization of tensorized electric field integral equation operators.