Multi-discretization domain specific language and code generation for differential equations

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.

Automated summary

FINCH, a domain specific language and code generation framework, is showcased for solving PDE problems including the advection diffusion equation and the phonon Boltzmann transport equation. It explores both finite volume and finite element methods. The recent developments in solving nonlinear equations using automatic and symbolic differentiation are also discussed, along with demonstration of the capability for the Bratu equation.