Adaptive Cross Approximation for MOM Matrix Fill for PC Problem Sizes to 157000 Unknowns

Abstract

Recent work on Sparse MOM codes for PC applications has reduced LU matrix factorization time to significantly less than matrix fill for problem unknowns approaching 200,000. This paper reports on the use and results of applying the recently developed Adaptive Cross Approximation for significantly reducing MOM matrix fill time. Results suggest that when problem sizes approach 500,000 unknowns, matrix fill can be reduced from 100 to 10 hours on a modern PC.

Direct Solve of Electrically Large Integral Equations for Problem Sizes to 1 M Unknowns

“…The Adaptive Cross Approximation (ACA) algorithm as recently developed by Bebendorf [2] and further discussed by [1,[3][4][5][6]9] is just such an approach.…”

“…Another "fast" solution is the Simply Sparse approach [7][8][9], which takes a change of basis approach. The MOM basis and test functions are transformed using unitary orthogonal matrices.…”

“…A number of authors [1][2][3][4][5]9] have now reported use of this ACA technique for filling system matrix blocks, including this author. It was during the work reported in [9], that it was observed that when the unknowns are spatially grouped, not only were the offdiagonal blocks of Z compressible, but also the off-diagonal blocks of the LU factored matrix were of compressible.…”

“…It was during the work reported in [9], that it was observed that when the unknowns are spatially grouped, not only were the offdiagonal blocks of Z compressible, but also the off-diagonal blocks of the LU factored matrix were of compressible. This later observation then raised the question: Could the ACA be used to directly LU factor and solve the system equations without explicit matrix fill?…”

Fast Direct Solution of Electromagnetic Scattering from Left-Handed Materials Coated Target over Wide Angle

“…The impedance matrix in (10) is composed of multiple submatrices, and the off-diagonal blocks are of low rank and can be compressed. In literature [17,18], Shaeffer points out that the upper triangular matrix U and multiple plane wave excitation RHS voltage matrix V also have low rank characteristics and can be compressed too, so the compression operation can be used for all steps of the solutions including impedance filling, LU factorization, and LU solving. In numerous matrix compression methods, the ACA algorithm in literature [19] is widely used [20][21][22].…”