A 2Level Domain Decomposition Preconditioner for KKT Systems with HeatEquation Constraints
Abstract
Solving optimization problems with transient PDEconstraints is computationally costly due to the number of nonlinear iterations and the cost of solving largescale KKT matrices. These matrices scale with the size of the spatial discretization times the number of time steps. We propose a new two level domain decomposition preconditioner to solve these linear systems when constrained by the heat equation. Our approach leverages the observation that the Schurcomplement is elliptic in time, and thus amenable to classical domain decomposition methods. Further, the application of the preconditioner uses existing time integration routines to facilitate implementation and maximize software reuse. The performance of the preconditioner is examined in an empirical study demonstrating the approach is scalable with respect to the number of time steps and subdomains.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.04421
 arXiv:
 arXiv:2305.04421
 Bibcode:
 2023arXiv230504421C
 Keywords:

 Mathematics  Numerical Analysis
 EPrint:
 8 pages