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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Automating GPU Scalability for Complex Scientific Models: Phonon Boltzmann Transport Equation
Heterogeneous computing environments combining CPU and GPU resources provide a great boost to large-scale scientific computing applications. Code generation utilities that partition the work into CPU and GPU tasks while considering data movement costs allow researchers to develop high-performance solutions more quickly and easily, and make these resources accessible to a larger user base.We present developments for a domain-specific language (DSL) and code generation framework for solving partial differential equations (PDEs). These enhancements facilitate GPU-accelerated solution of the Boltzmann transport equation (BTE) for phonons, which is the governing equation for simulating thermal transport in semiconductor materials at sub-micron scales. The solution of the BTE involves thousands of coupled PDEs as well as complicated boundary conditions and solving a nonlinear equation that couples all of the degrees of freedom at each time step. These developments enable the DSL to generate configurable hybrid GPU/CPU code that couples accelerated kernels with user-defined code. We observed performance improvements of around 18X compared to a CPU-only version produced by this same DSL with minimal additional programming effort.
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- Award ID(s):
- 2004236
- PAR ID:
- 10556067
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 979-8-3503-8711-7
- Page Range / eLocation ID:
- 430 to 439
- Format(s):
- Medium: X
- Location:
- San Francisco, CA, USA
- Sponsoring Org:
- National Science Foundation
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