TY - GEN

T1 - Toward more geometrically adaptive compression of moment matrices

AU - Brick, Yaniv

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - In recent years, fast direct integral equation solvers have been developed, as an alternative to iterative solver, for problems that suffer from ill-conditioning or when a solution is sought for many right-hand-sides. These solvers rely on the fast computation of a compressed representation of the impedance matrix. Then, the compressed representation's factorized (effectively 'solved') form is computed and applied to each right-hand-side. If the factorized form inherits the original matrix's compressibility, the savings in memory are maintained and the solution for each right-hand-side is, indeed, fast. The compression of the impedance matrix is often performed in a hierarchical manner. The geometry is first partitioned into clusters of basis and testing functions. Then, a hierarchical block structure for compression is defined, in accordance with the choice of hierarchical algebraic procedure for computing the compressed factorized form, e.g., [1], [2], or [3]. Matrix blocks, corresponding to interactions between sources and observers, that are assumed compressible, in some sense, are identified and compressed.

AB - In recent years, fast direct integral equation solvers have been developed, as an alternative to iterative solver, for problems that suffer from ill-conditioning or when a solution is sought for many right-hand-sides. These solvers rely on the fast computation of a compressed representation of the impedance matrix. Then, the compressed representation's factorized (effectively 'solved') form is computed and applied to each right-hand-side. If the factorized form inherits the original matrix's compressibility, the savings in memory are maintained and the solution for each right-hand-side is, indeed, fast. The compression of the impedance matrix is often performed in a hierarchical manner. The geometry is first partitioned into clusters of basis and testing functions. Then, a hierarchical block structure for compression is defined, in accordance with the choice of hierarchical algebraic procedure for computing the compressed factorized form, e.g., [1], [2], or [3]. Matrix blocks, corresponding to interactions between sources and observers, that are assumed compressible, in some sense, are identified and compressed.

UR - http://www.scopus.com/inward/record.url?scp=85074901511&partnerID=8YFLogxK

U2 - 10.1109/ICEAA.2019.8879029

DO - 10.1109/ICEAA.2019.8879029

M3 - Conference contribution

AN - SCOPUS:85074901511

T3 - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

SP - 513

BT - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

Y2 - 9 September 2019 through 13 September 2019

ER -