Least squares and domain decomposition methods applied to the numerical solution of nonlinear problems in fluid dynamics

Finite element approximations to handle complicated geometries; nonlinear least squares formulations; conjugate gradient methods with scaling to solve the least squares problems; and subdomain decomposition to reduce the solution of very large problems to the solution of problems of the same type but on smaller domains using vector processors are discussed. Coupling of nonlinear least squares methods with arc length continuation is considered. The full potential equation for compressible inviscid transonic flows and the Navier-Stokes for incompressible viscous flows are solved via finite element approximations. Domain decomposition methods implementation on a computer system with parallel processing possibilities is outlined. Numerical experiments results are presented.