Code generation for 3D partial differential equation models from a high-level functional intermediate language

Partial Differential Equation (PDE) modelling is an important tool in scientific domains for bridging theory with reality; however, they can be complex to program and even more difficult to abstract. The evolving parallel computing landscape is also making it increasingly difficult to write and maintain codes (such as PDE models) which retain performance across different parallel platforms. Computational scientists should be able to focus on their science instead of also having to become high performance computing experts in order to take advantage of faster parallel hardware. Current methods targeting this problem either concentrate on very niche applications, are too simplistic for real world problems or are too low-level to be easily programmable. Domain Specific Languages (DSLs) are a popular approach, but they have two opposing goals: improving programmability, while also providing high performance. This thesis presents a solution for developing performance portable 3D PDE models, using room acoustics simulations as a case study, by raising the abstraction level in the existing hardware-agnostic, intermediary language LIFT. This functional language and compiler is designed for DSLs to compile into and provides a separation of concerns for developing parallel applications. This separation enables DSL writers to focus on developing high-level abstractions providing productivity to the user, while LIFT turns the intermediary parallel representation these abstractions compile down to into hardware-optimised code. A suite of composable, algorithmic primitives enables LIFT to reuse functionality across domains and an exploratory search space provides a way to find the best optimisations for a given platform. As this thesis shows, room acoustic simulations are expressible in LIFT with only a few small changes to the framework. These expressions are able to achieve comparable or better performance to original hand-written benchmarks. Furthermore, such expressions enable room acoustics models to run across multiple platforms and easily swap in optimisations. Being able to test out what optimisations give the best performance for a given platform — without rewriting or retuning — allows computational scientists to focus on their own work. Optimisations previously inaccessible in LIFT are developed that target 3D stencils generally, including 3D PDE models. In particular, 2.5D Tiling and compiler passes to inline private arrays and structs are added to the LIFT ecosystem, giving high performance to various 3D stencil codes. The 2.5D Tiling optimisation is coded functionally for the first time in LIFT and is selected automatically by additional rewrite rules. These rewrite rules, such as the one for 2.5D Tiling, are explored in a search space to find the best set of optimisations for an application on a given platform. Building on previous work, LIFT is extended to enable complex boundary conditions and room shapes for room acoustics models. This is the first intermediate representation in a high-level code generator to do so. Additionally, it is also the first high-level framework to support frequency-dependent boundary handling for room acoustics simulations. Combined, these contributions show that high-level abstractions for 3D PDE models are possible, enabling computational scientists to optimise and parallelise their codes more easily across different parallel platforms