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首頁> 外文期刊>Computer Methods in Applied Mechanics and Engineering >An implicit block ILU smoother for preconditioning of Newton-Krylov solvers with application in high-order stabilized finite-element methods
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An implicit block ILU smoother for preconditioning of Newton-Krylov solvers with application in high-order stabilized finite-element methods

機譯：用于牛頓-克里洛夫求解器預(yù)處理的隱式塊ILU平滑器及其在高階穩(wěn)定有限元方法中的應(yīng)用

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This paper presents an efficient and highly-parallelizable preconditioning technique for Newton-Krylov solvers. The proposed method can be viewed as a generalization of the implicit line smoothing technique by extending the groups of implicitly-solved unknowns from lines to blocks. The blocks are formed by partitioning the computational domain such that the strong connections between unknowns are not broken by the partition boundaries. The ILU algorithm is used to obtain an approximate (or exact) factorization for each block. Then, a block-Jacobi iteration is formulated in which the degrees of freedom within the blocks are solved implicitly. To stabilize the iterations for high-CFL systems, a dual-CFL strategy, with a lower CFL in the preconditioner matrix, is developed. The performance of the proposed method as a linear preconditioner is demonstrated for second- and third-order steady-state solutions of Reynolds-Averaged Navier-Stokes (RANS) equations on the NASA Common Research Model (CRM), including the high-lift configuration. For the studied test cases, it is shown that in comparison with the traditional ILU(k) method, the proposed preconditioner requires significantly less memory and it can result in notably faster solutions. (C) 2019 Elsevier B.V. All rights reserved.
機譯：本文提出了一種適用于牛頓-克里洛夫求解器的高效且高度可并行化的預(yù)處理技術(shù)。通過將隱式求解的未知項從線擴展到塊，可以將所提出的方法視為對隱式線平滑技術(shù)的概括。通過劃分計算域來形成塊，使得未知數(shù)之間的強連接不會被劃分邊界破壞。 ILU算法用于獲取每個塊的近似（或精確）分解。然后，制定了塊雅各比迭代，其中隱式求解了塊內(nèi)的自由度。為了穩(wěn)定高CFL系統(tǒng)的迭代，開發(fā)了在預(yù)調(diào)節(jié)器矩陣中具有較低CFL的雙重CFL策略。在NASA通用研究模型（CRM）上，包括高舉配置下，針對雷諾平均Navier-Stokes（RANS）方程的二階和三階穩(wěn)態(tài)解，證明了該方法作為線性預(yù)處理器的性能。 。對于研究的測試案例，結(jié)果表明，與傳統(tǒng)的ILU（k）方法相比，所提出的預(yù)處理器所需的內(nèi)存明顯更少，并且可以顯著提高解決方案的速度。 （C）2019 Elsevier B.V.保留所有權(quán)利。

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