1. Multiply gauged solution initialization with steepest descent smoothing
- Author
-
Sanjiv M. Sansgiri, Joe Padovan, and Lala B. Krishna
- Subjects
Iterative method ,Applied Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Initialization ,Computer Science::Numerical Analysis ,Computer Science Applications ,Multigrid method ,Computational Theory and Mathematics ,Conjugate gradient method ,Method of steepest descent ,Gradient descent ,Algorithm ,Smoothing ,Sparse matrix ,Mathematics - 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 de...
- Published
- 1994