通过自适应BDDC和Krylov子空间回收加速不稳流模拟
Speeding up an unsteady flow simulation by adaptive BDDC and Krylov subspace recycling
AI总结：
本文通过自适应BDDC和Krylov子空间回收技术，显著加速了不稳流模拟中大规模线性方程组的求解，节省了超过40%的计算时间。
摘要：
我们处理通过预条件共轭梯度法（PCG）求解一系列大规模线性方程组的加速问题。这些方程组来源于不稳不可压缩流模拟中的时间推进。我们应用压力校正方案，并专注于压力校正器的泊松问题求解。其可扩展求解是许多应用中的主要计算挑战。问题的右端在每个时间步变化，而系统矩阵是常数且对称正定。我们针对流绕单位球体的代表性问题研究了加速技术。我们的基线方法是通过非重叠域分解法并行求解每个问题。接口问题通过PCG与三级BDDC预条件子求解。作为初步步骤，选择了一个合适的PCG迭代停止准则。接下来，逐步添加了两种加速求解的技术。在PCG中使用消去法，结合几种Krylov子空间回收方法。最后，在三级BDDC方法中添加了粗空间的自适应选择。论文包含丰富的实验，并对并行超级计算机上的计算时间进行了仔细测量。加速技术的结合最终导致计算时间节省超过40%。
英文摘要：
We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We apply a pressure correction scheme and focus on the solution of the Poisson problem for the pressure corrector. Its scalable solution presents the main computational challenge in many applications. The right-hand side of the problem changes in each time step, while the system matrix is constant and symmetric positive definite. The acceleration techniques are studied on a representative problem of flow around a unit sphere. Our baseline approach is based on a parallel solution of each problem in the sequence by nonoverlapping domain decomposition method. The interface problem is solved by PCG with the three-level BDDC preconditioner. As a preliminary step, an appropriate stopping criterion for the PCG iterations is chosen. Next, two techniques for accelerating the solution are gradually added to the baseline approach. Deflation is used within PCG with several approaches to Krylov subspace recycling. Finally, we add the adaptive selection of the coarse space within the three-level BDDC method. The paper is rich in experiments with careful measurements of computational times on a parallel supercomputer. The combination of the acceleration techniques eventually leads to saving more than 40 % of the computational time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
