Grid-based fluid simulations are often limited in resolution by their high memory usage and computational costs. One approach to reducing memory usage and computational costs is to vary the grid resolution over the spatial domain. We introduce DCGrid, a new data structure for fluid simulations. DCGrid is suited for instantiation in GPU memory and allows for varying resolution over the spatial domain. We developed an efficient, optimization-based method for local mesh refinement that automatically adapts the grid resolution according to user-defined parameters during simulations. Additionally, we complement our data structure with an efficient scheme for approximate handling of collisions between fluid and static solids on cells with varying resolutions. We integrate DCGrid in a cloud simulation and extend a terrain-atmosphere interaction model to work with cells of varying resolution and rapidly changing conditions. Furthermore, we demonstrate the performance of our new methods on both simple simulations of smoke flow and complex simulations of weather phenomena and compare them to similar fluid simulations on state-of-the-art adaptive grid structures.

Null pointer dereferences in Java raise exceptions, occur often, are hard to debug and cost a lot of unnecessary effort and resources. Therefore, a lot of effort has been put in analyses spotting those null pointer dereferences. As developers rely on those analyses it is important that they are sound. However, proving null pointer analyses sound has been a complex problem. Hence, we developed a nullness analysis for Java that is provably sound. The analysis is built as an abstract interpreter upon the sturdy framework, that allows for compositional soundness proofs. This reduces the proof effort greatly. By creating a concrete interpreter, and by generating arbitrary programs, we were able to assess the soundness of the nullness analysis to great extend. Also, we have proven a part of the analysis to be sound in a formal way.