Symmetric Near-Field Schur Complement Preconditioner for Hierarchal Electric Field Integral Equation Solve

TL;DR

This paper introduces a symmetric near-field Schur complement preconditioner for Hierarchal EFIE solvers, significantly reducing memory and computation time while maintaining effectiveness, and demonstrating notable speed-ups in iterative solutions.

Contribution

It proposes a novel symmetric near-field Schur complement preconditioner that improves efficiency and reduces memory usage for Hierarchal EFIE solutions.

Findings

Achieves near-linear complexity in setup and solve times.

Reduces preconditioner setup time by half using symmetry.

Demonstrates 1.5-2.3x speed-up over existing preconditioners.

Abstract

In this paper, a robust and effective preconditioner for the fast Method of Moments(MoM) based Hierarchal Electric Field Integral Equation(EFIE) solver is proposed using symmetric near-field Schur's complement method. In this preconditioner, near-field blocks are scaled to a diagonal block matrix and these near-field blocks are replaced with the scaled diagonal block matrix which reduces the near-field storage memory and the overall matrix vector product time. Scaled diagonal block matrix is further used as a preconditioner and due to the block diagonal form of the final preconditioner, no additional fill-ins are introduced in its inverse. The symmetric property of the near-field blocks is exploited to reduce the preconditioner setup time. Near linear complexity of preconditioner set up and solve times is achieved by near-field block ordering, using graph bandwidth reduction algorithms and compressing the fill-in blocks in preconditioner computation. Preconditioner set up time is reduced to half by using the symmetric property and near-field block ordering. It has been shown using a complexity analysis that the cost of preconditioner construction in terms of computation and memory is linear. Numerical experiments demonstrate an average of 1.5-2.3x speed-up in the iterative solution time over Null-Field based preconditioners.