BLAS IV: A BLAS for Rk Matrix Algebra

Authors

  • John Shaeffer Matrix Compression Technologies, LLC Marietta, Georgia

Keywords:

direct factor method of moments, low rank matrix algebra and electromagnetic scattering

Abstract

Basic Linear Algebra Subroutines (BLAS) are well-known low-level workhorse subroutines for linear algebra vector-vector, matrixvector and matrix-matrix operations for full rank matrices. The advent of block low rank (Rk) full wave direct solvers, where most blocks of the system matrix are Rk, an extension to the BLAS III matrix-matrix work horse routine is needed due to the agony of Rk addition. This note outlines the problem of BLAS III for Rk LU and solve operations and then outlines an alternative approach, which we will call BLAS IV. This approach utilizes the thrill of Rk matrix-matrix multiply and uses the Adaptive Cross Approximation (ACA) as a methodology to evaluate sums of Rk terms to circumvent the agony of low rank addition.

Downloads

Download data is not yet available.

References

J. Shaeffer, “Direct solve of electrically large integral equations for problem sizes to 1 M unknowns,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2306-2313, Aug. 2008.

J. Shaeffer, “Low rank Matrix Algebra for the method of moments,” ACES Journal, Oct. 2018.

M. Bebendorf, Hierarchical Matrices, Berlin, Springer-Verlag, 2008.

J. Shaeffer, “Direct solve of electrically large integral equations for

problem Sizes to 1M unknowns,” NASA/CR-2008-215353, Sept. 2008.

J. Shaeffer, “Five million unknown MOM LU factorization on a PC workstation,” Antenna Measurement Techniques Association Meeting, Long Beach, CA, Oct. 11-16, 2015.

Downloads

Published

2020-11-07

How to Cite

John Shaeffer. (2020). BLAS IV: A BLAS for Rk Matrix Algebra. The Applied Computational Electromagnetics Society Journal (ACES), 35(11), 1266–1267. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/7459

Issue

Section

Articles