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We present a high-level domain-specific language (DSL) interface to drive an adaptive incomplete $k$-d tree-based framework for finite element (FEM) solutions to PDEs. This DSL provides three key advances: (a) it abstracts out the complexity of implementing non-trivial FEM formulations, (b) it simplifies deploying these formulations on arbitrarily complicated and adaptively refined meshes, and (c) it exhibits good parallel performance. Taken together, the DSL interface allows end-users to rapidly and efficiently prototype new mathematical approaches, and deploy them on large clusters for solving practical problems. We illustrate this DSL by implementing a workflow for solving PDEs using the recently developed shifted boundary method (SBM). The SBM requires approximating relatively complicated integrals over boundary surfaces. Using a high-level DSL greatly simplifies this process and allows rapid exploration of variations. We demonstrate these tools on a variety of 2-D and 3-D configurations. With fewer than 20 lines of input, we can produce a parallel code that scales well to thousands of processes. This generated code is made accessible and readable to be easily modified and hand-tuned, making this tool useful even to experts with the target software.

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 more quickly and easily develop high-performance solutions, 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 nonlinear processing 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.