TY - JOUR

T1 - Sparse tensor edge elements

AU - Hiptmair, Ralf

AU - Jerez-Hanckes, Carlos

AU - Schwab, Christoph

N1 - Funding Information:
C. Jerez-Hanckes’s work was partially funded by FONDECYT 11121166 and CONICYT project Anillo ACT1118 (ANANUM).
Funding Information:
The work of C. Schwab was partially supported by the European Research Council under grant number ERC AdG 247277-STAHDPDE.

PY - 2013/12

Y1 - 2013/12

N2 - 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.

AB - 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.

KW - Commuting diagram property

KW - Edge elements

KW - Fortin projector

KW - Maxwell cavity source problem

KW - Sparse tensor approximation

KW - Stochastic source problems

UR - http://www.scopus.com/inward/record.url?scp=84888135977&partnerID=8YFLogxK

U2 - 10.1007/s10543-013-0435-3

DO - 10.1007/s10543-013-0435-3

M3 - Article

AN - SCOPUS:84888135977

VL - 53

SP - 925

EP - 939

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 4

ER -