In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm.