In designing efficient algorithms to simulate dynamic concentration profiles using the Gaussian puff model there are two main use cases we will consider: calculation at a small number of specified sensor locations, and calculation on a regular, rectangular grid. It is often only desirable to compute concentrations at specific locations to simulate concentration readings from a point-in-space sensor. In this context, we can leverage equation (2) to determine for which sensor locations we expect a non-zero concentration reading. Additionally, it can be useful to simulate the model on a dense 3D grid since this spatially-dense data enables 3D visualizations and can be used to solve relevant optimization problems, e.g finding a sensor arrangement that maximizes the likelihood of emission detection. Again we can leverage equation ( ) to design a fast method for grid-based simulations. In the following sections, we discuss implementation details to optimize the model for both sparsely placed sensor locations and grid-based applications. We'll begin by describing the grid-based method and state the sensor-based method as a specialization.