Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition

Schur Complement based domain decomposition preconditioners with Low-rank corrections

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this “Schur Low Rank” (SLR) preconditioning approach, the coefficient matrix is first decoupled by DD, and then a low-rank correction is exploited to compute an approximate inverse of the Schur compleme...

A preconditioner for the Schur complement domain decomposition method

Accelerating simulation of ensembles of locally differing optical structures via a Schur complement domain decomposition.

We present a Schur complement domain decomposition method that can significantly accelerate simulation of ensembles of locally differing optical structures. We apply the method to design a multi-spatial-mode photonic crystal waveguide splitter that exhibits high transmission and preservation of modal content, showing design acceleration by more than a factor of 20.

Direct Schur Complement Method by Domain Decomposition Based on H-Matrix Approximation

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(NΓ log NΓ) is almost linear in NΓ – the number of de...

The condition number of the Schur complement in domain decomposition

In the nonoverlapping approach to domain decomposition (cf. [10], [21] and the references therein) the nite element equation for an elliptic boundary value problem is reduced, after parallel subdomain solves, to its Schur complement which involves only the nodal variables (degrees of freedom) on the subdomain boundaries. The condition number of the Schur complement has been investigated for sec...