Philosophy of Science Commons^™

Linearly Preconditioned Nonlinear Solvers For Phase Field Equations Involving P-Laplacian Terms, Wenqiang Feng

Doctoral Dissertations

Phase field models are usually constructed to model certain interfacial dynamics. Numerical simulations of phase-field models require long time accuracy, stability and therefore it is necessary to develop efficient and highly accurate numerical methods. In particular, the unconditionally energy stable , unconditionally solvable, and accurate schemes and fast solvers are desirable.

In this thesis, We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical …