Multiply gauged solution initialization with steepest descent smoothing

Abstract

This paper develops an algorithmic scheme to determine initial/starting solutions for iterative linear equation solvers, i.e. preconditioned conjugate gradient, multigrid, SOR and Chebeshev semi-iterative. Employing symbolic operators, multi parameter gauges are introduced to enable individual partition level functional fits of domain decomposed problems. Such gauges are metered by a global minimization of the appropriate energy norm. To remove functional discontinuities on subdomain interfaces, successive applications of a partitioned steepest descent algorithm are employed as a smoothing step. The combination of partitioned initialization and iterative smoothing lead to a robust algorithmic pairing which can provide very accurate starting values for very large simulations. If successively iterated in a series of initialization—steepest descent smoothing cycles, the combined scheme can yield converged results in less iterations than the PCG. This is illustrated by a variety of benchmark examples which demonstrate the sensitivity of the scheme to partitioning, operator type and geometric topology.

Keywords:

• Linear systems
• iterative matrix inversion
• sparse large systems
• multiply gauged itialization
• steepest descent smoothing

C.R Categories:

• G.1.0
• G.1.2
• G.1.3