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Finch, a domain specific language and code generation framework for partial differential equations (PDEs), is demonstrated here to solve two classical problems: steady-state advection diffusion equation (single PDE) and the phonon Boltzmann transport equation (coupled PDEs). Both finite volume and finite element methods are explored. In addition to work presented at the 2022 International Conference on Computational Science (Heisler et al., 2022), we include recent developments for solving nonlinear equations using both automatic and symbolic differentiation, and demonstrate the capability for the Bratu (nonlinear Poisson) equation.
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Finch: Domain Specific Language and Code Generation for Finite Element and Finite Volume in Julia
We introduce FINCH, a Julia-based domain specific language (DSL) for solving partial differential equations in a discretization agnostic way, currently including finite element and finite volume methods. A key focus is code generation for various internal or external software targets. Internal targets use a modular set of tools in Julia providing a direct solution within the framework. In contrast, external code generation produces a set of code files to be compiled and run with external libraries or frameworks. Examples include a matlab target, for smaller problems or prototyping, or C++/MPI based targets for larger problems needing scalability. This allows us to take advantage of their capabilities without needlessly duplicating them, and provides options tailored to the needs of the domain scientist. The modular design of FINCH allows ongoing development of these target modules resulting in a more extensible framework and a broader set of applications. The support for multiple discretizations, including finite element and finite volume methods, also contributes to this goal. Another focus of this project is complex systems containing a large set of coupled PDEs that could be challenging to efficiently code and optimize by hand, but that are relatively simple to specify using the DSL. In this paper we present the key features of FINCH that set it apart from many other DSL options, and demonstrate the basic usage and current capabilities through examples.
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- PAR ID:
- 10431977
- Date Published:
- Journal Name:
- Computational Science -- ICCS 2022
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-031-08751-6_9
