Mat2Boundary: Treating User-Defined Boundary Condition as SpMV for Distributed PDE Solvers on Block-Structured Grids
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913129211887616 |
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| author | Cai, Yanzheng Zhang, Mingzhe Chen, Shengqi Song, Haoyuan Chen, Wenguang |
| author_facet | Cai, Yanzheng Zhang, Mingzhe Chen, Shengqi Song, Haoyuan Chen, Wenguang |
| contents | Boundary-condition (BC) handling is a major source of complexity in PDE solvers on structured and block-structured grids, especially for high-order methods and distributed-memory execution. We present Mat2Boundary, a DSL and compiler for boundary computations that models a broad class of boundary-conditions as affine sparse linear operators. This abstraction unifies halo copying, circular and symmetric mappings, zero padding, block-edge synchronization, and user-defined interpolation, while exposing a modular basic sub-matrix interface for declarative composition. To make this representation efficient, Mat2Boundary combines multi-stage programming and polyhedral analysis to generate matrix-free kernels for structured cases, support user-defined sparse matrices for irregular cases, eliminate redundant boundary work, and synthesize reusable communication schedules for distributed execution. Evaluated on two shallow-water equation solvers on cubed-sphere grids and HPCG, Mat2Boundary achieves up to 7.6$\times$ BC-kernel speedup, reduces BC code by over 70%, and scales to 1,344 CPU cores with 72%-88% efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14780 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mat2Boundary: Treating User-Defined Boundary Condition as SpMV for Distributed PDE Solvers on Block-Structured Grids Cai, Yanzheng Zhang, Mingzhe Chen, Shengqi Song, Haoyuan Chen, Wenguang Programming Languages Distributed, Parallel, and Cluster Computing Boundary-condition (BC) handling is a major source of complexity in PDE solvers on structured and block-structured grids, especially for high-order methods and distributed-memory execution. We present Mat2Boundary, a DSL and compiler for boundary computations that models a broad class of boundary-conditions as affine sparse linear operators. This abstraction unifies halo copying, circular and symmetric mappings, zero padding, block-edge synchronization, and user-defined interpolation, while exposing a modular basic sub-matrix interface for declarative composition. To make this representation efficient, Mat2Boundary combines multi-stage programming and polyhedral analysis to generate matrix-free kernels for structured cases, support user-defined sparse matrices for irregular cases, eliminate redundant boundary work, and synthesize reusable communication schedules for distributed execution. Evaluated on two shallow-water equation solvers on cubed-sphere grids and HPCG, Mat2Boundary achieves up to 7.6$\times$ BC-kernel speedup, reduces BC code by over 70%, and scales to 1,344 CPU cores with 72%-88% efficiency. |
| title | Mat2Boundary: Treating User-Defined Boundary Condition as SpMV for Distributed PDE Solvers on Block-Structured Grids |
| topic | Programming Languages Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2605.14780 |