TY - GEN
T1 - Primal and dual wavelets for fast electric field integral equation solutions on unstructured meshes
AU - Adrian, Simon B.
AU - Andriulli, Francesco P.
AU - Eibert, Thomas F.
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/10/18
Y1 - 2017/10/18
N2 - This works presents a solenoidal wavelet basis for both structured and unstructured meshes to complement the existing non-solenoidal wavelet basis for preconditioning the electric field integral equation (EFIE). Standard loop functions are classically used to complement a non-solenoidal wavelet basis resulting in a condition number that grows with O(1=h), where h is the average length of the mesh. With the new solenoidal wavelet basis we provably yield a condition number that grows as O(log2(1=h)). We obtain this result by leveraging on an explicit inverse of the dual Haar wavelet transformation matrix and on the scalar Calderón identity. Numerical results corroborate the presented theory and show the practical applicability of the proposed approach.
AB - This works presents a solenoidal wavelet basis for both structured and unstructured meshes to complement the existing non-solenoidal wavelet basis for preconditioning the electric field integral equation (EFIE). Standard loop functions are classically used to complement a non-solenoidal wavelet basis resulting in a condition number that grows with O(1=h), where h is the average length of the mesh. With the new solenoidal wavelet basis we provably yield a condition number that grows as O(log2(1=h)). We obtain this result by leveraging on an explicit inverse of the dual Haar wavelet transformation matrix and on the scalar Calderón identity. Numerical results corroborate the presented theory and show the practical applicability of the proposed approach.
UR - https://www.scopus.com/pages/publications/85042213174
U2 - 10.1109/APUSNCURSINRSM.2017.8072404
DO - 10.1109/APUSNCURSINRSM.2017.8072404
M3 - Conference contribution
AN - SCOPUS:85042213174
T3 - 2017 IEEE Antennas and Propagation Society International Symposium, Proceedings
SP - 723
EP - 724
BT - 2017 IEEE Antennas and Propagation Society International Symposium, Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, APSURSI 2017
Y2 - 9 July 2017 through 14 July 2017
ER -