FEniCSx-pctools：FEniCSx中用于PETSc块线性代数预条件的工具
FEniCSx-pctools: Tools for PETSc block linear algebra preconditioning in FEniCSx
AI总结：
该研究推出FEniCSx-pctools软件包，可简化FEniCSx中PETSc块预条件策略的配置，自动附加元数据以适配不同组装系统，经多类示例与8192进程并行测试验证，适用于大规模偏微分方程求解。
摘要：
使用有限元法求解偏微分方程会产生必须求解的大型线性方程组。当这些系统因包含多场变量而具有天然块结构时，为实现高效且可扩展的求解过程，采用搭配精心设计、能利用底层物理结构的预条件策略的迭代求解器就十分必要。FEniCSx预条件工具（FEniCSx-pctools）是一款软件包，可简化在基于FEniCS项目的DOLFINx有限元求解器组装的线性系统上指定PETSc（便携式可扩展科学计算工具包）块预条件策略的流程。该软件包会自动附加所有必要的元数据，使得预条件策略可通过PETSc的标准选项数据库应用于整体组装和分块组装的系统。其附带的文档化示例包括一个简单的混合泊松系统，以及用于Navier-Stokes方程预条件的更复杂的压力对流扩散方法。我们在完全耦合的温度-Navier-Stokes系统上展示了弱并行可扩展性，测试规模最高达8192个MPI（消息传递接口）进程，证明了该方法适用于大规模问题。
英文摘要：
Solving partial differential equations with the finite element method leads to large linear systems of equations that must be solved. When these systems have a natural block structure due to multiple field variables, using iterative solvers with carefully designed preconditioning strategies that exploit the underlying physical structure becomes necessary for an efficient and scalable solution process. FEniCSx Preconditioning Tools (FEniCSx-pctools) is a software package that eases the specification of PETSc (Portable, Extensible Toolkit for Scientific Computation) block preconditioning strategies on linear systems assembled using the DOLFINx finite element solver of the FEniCS Project. The package automatically attaches all necessary metadata so that preconditioning strategies can be applied via PETSc's standard options database to monolithic and block assembled systems. The documented examples include a simple mixed Poisson system and more complex pressure convection-diffusion approach to preconditioning the Navier-Stokes equations. We show weak parallel scaling on a fully coupled temperature-Navier-Stokes system up to 8192 MPI (Message Passing Interface) processes, demonstrating the applicability of the approach to large-scale problems.
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