Mat2Stencil: A Modular Matrix-Based DSL for Explicit and Implicit Matrix-Free PDE Solvers on Structured Grid

Explore a groundbreaking domain-specific language (DSL) called Mat2Stencil in this 15-minute conference talk from OOPSLA2 2023. Discover how this innovative DSL and its compiler revolutionize the development of partial differential equation (PDE) solvers on structured grids. Learn about the structured sparse matrix abstraction that enables modular and flexible expression of solvers, including Jacobi and Gauss-Seidel preconditioners, incomplete LU or Cholesky decompositions, and multigrid methods. Understand the matrix-free code generation process using generalized stencils and multi-stage programming. Delve into the novel automatic parallelization technique for spatially dependent loops, offering compile-time deterministic task partitioning and efficient multi-threaded implementation. Examine the performance results of Mat2Stencil implementations compared to manual implementations across various benchmarking programs, including NAS Parallel Benchmarks and High Performance Conjugate Gradients.