We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations, repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x.

翻译：本文提出一种针对三角形网格产生的线性系统量身定制的快速稀疏矩阵置换算法。我们的方法能够生成嵌套剖分类的置换，同时显著降低置换过程的运行时开销。该算法并非强制要求严格的平衡性和分隔子最优性，而是有意放宽这些设计决策，以优先实现快速划分和高效的消去树构建。我们的方法将置换分解为块级局部排序和分隔子的紧凑商图排序，既保留了稀疏Cholesky分解所需的基本结构，又避免了其最耗时的组成部分。我们将该算法集成到CPU和GPU上由厂商维护的稀疏Cholesky求解器中。在一系列图形应用（包括单次分解和重复分解）中，我们的方法将置换时间减少了高达6.27倍，并提升了稀疏Cholesky求解性能。