A Domain Specific Language Applied to Phonon Boltzmann Transport for Heat Conduction

Abstract

The phonon Boltzmann transport equation is a good model for heat transfer in nanometer scale structures such as semiconductor devices. Computational complexity is one of the main challenges in numerically solving this set of potentially thousands of nonlinearly coupled equations. Writing efficient code will involve careful optimization and choosing an effective parallelization strategy, requiring expertise in high performance computing, mathematical methods, and thermal physics. To address this challenge, we present the domain specific language and code generation software Finch. This language allows a domain scientist to enter the equations in a simple format, provide only basic mathematical functions used in the model, and generate efficient parallel code. Even very complex systems of equations such as phonon Boltzmann transport can be entered in a very simple, intuitive way. A feature of the framework is flexibility in numerical methods, computing environments, parallel strategies, and other aspects of the generated code. We demonstrate Finch on this problem using a variety of parallel strategies and model configurations to demonstrate the flexibility and ease of use.