Implementation Overview

An important aspect of Kona’s implementation is that it makes no assumptions regarding the dimension, type, or parallelization of the state variables. In other words, state variables are assumed to exist in an abstract vector space.

For ease of use, Kona provides a default NumPy implementation for this vector space. For high-performance applications, where variables are typically distributed across multiple processes, the user must implement the storage and linear algebra operations for the vector space. This model allows Kona to be used in a variety of parallel environments, because it remains agnostic to how the user defines, stores, and manipulates the vectors.

However this abstraction only exists for the state-space. For design variables and constraints, it is assumed that the vector spaces never become too large for a single process. Consequently, design and constraint vector spaces are locked into the default NumPy implementation. This allows Kona to exploit various explicit-algebra tools that significantly impove the functionality and efficiency of its optimization algorithms.

Additionally, Kona separates optimization algorithms from the underlying PDE solver such that any new optimization algorithm can be implemented in Kona using Kona’s own abstracted vector classes. This allows for rapid development and testing of new algorithms independently from the PDE solver, and guarantees that any solver that has already been integrated with Kona will work correctly underneath any new algorithm that may be added in the future.