TY - JOUR A1 - Deuflhard, Peter T1 - The Grand Four. Affine Invariant Globalizations of Newton's Method JF - Vietnam Journal of Mathematics Y1 - 2018 U6 - https://doi.org/10.1007/s10013-018-0301-3 VL - 46 IS - 4 SP - 761 EP - 777 ER - TY - GEN A1 - Nägel, Arne A1 - Deuflhard, Peter A1 - Wittum, Gabriel T1 - Efficient Stiff Integration of Density Driven Flow Problems N2 - The paper investigates the efficient use of a linearly implicit stiff integrator for the numerical solution of density driven flow problems. Upon choosing a one-step method of extrapolation type (code LIMEX), the use of full Jacobians and reduced approximations are discussed. Numerical experiments include nonlinear density flow problems such as diffusion from a salt dome (2D), a (modified) Elder problem (3D), the saltpool benchmark (3D) and a real life salt dome problem (2D). The arising linear equations are solved using either a multigrid preconditioner from the software package UG4 or the sparse matrix solver SuperLU. T3 - ZIB-Report - 18-54 KW - stiff integration for PDEs KW - linearly implicit Euler discretization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70891 SN - 1438-0064 ER -