Joel Fenwick

Optimal paths for mutually visible agents

We present linear-time algorithms for a pair of robots to travel inside a simple polygon on paths of total minimum length while maintaining visibility with one another. We show that the optimal paths for this mutually visible constraint are almost always each agents shortest path. The this may not happen only on a sub-case of when the line of visibility of the source points crosses the line of visibility of the target points. We also show that the travel schedule is computable, but that it also suffers from a pathological case.

On lazy evaluation as a tool to optimize the efficiency of large scale numerical simulations in Python

Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees modelers from issues of optimized implementation and parallelization. In its current implementation escript evaluates expressions which define PDE coefficients immediately for all nodes or elements of an FEM mesh. In the paper we will demonstrate that for complex rheologies such as the Drucker-Prager plasticity model, the memory requirements for this strategy are the limiting factor for scaling up the mesh size. The python module is backed by an escript C++ library where the processing is performed. We will discuss an new extension to the PDE coefficient handling provided by this C++ library which uses a lazy evaluation technique and will demonstrate the efficiency of this new extension in terms of compute time and memory usage for a practical engineering application, namely the simulation of elastic-plastic, saturated porous media