Multilevel First-Order System Least Squares for Elliptic Grid Generation

Authors:
A. L. Codd;T. A. Manteuffel;S. F. McCormick;J. W. Ruge
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2003

Citing 0
Cited 4

First-order system least squares (FOSLS) for coupled fluid-elastic problems

Journal of Computational Physics
A unified least-squares formulation for fluid-structure interaction problems

Computers and Structures
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids

Computers & Mathematics with Applications
A Preconditioner for the Finite Element Approximation to the Arbitrary Lagrangian-Eulerian Navier-Stokes Equations

SIAM Journal on Scientific Computing

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Abstract

A new fully variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [A. L. Codd, T. A. Manteuffel, and S. F. McCormick, SIAM J. Numer. Anal., 41 (2003), pp. 2197--2209] that involves using Newton's method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equation. The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. The present paper verifies the assumptions of the companion work and confirms the overall efficiency of the scheme with numerical experiments.