Path following for Large Nonlinear Equations Byimplicit

An adaptive block elimination method based on recursive projection techniques is proposed for solving large linear systems which arise when applying Newton methods to parameter dependent nonlinear equations. The method is suitable for non-linear systems that have a Jacobian with a symmetric and almost positive deenite main block. The implicitly deened large symmetric and positive deenite subsystems are solved by conjugate gradient methods whereas the remaining low dimensional part is treated by a direct solver. Numerical examples coming from discretization of nonlinearly perturbed elliptic partial diierential equations as, e.g., the Bratu problem, show that the method works well.