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高分辨率全球非結(jié)構(gòu)網(wǎng)格生成實(shí)踐
2022年電子技術(shù)應(yīng)用第6期
劉 壯,,黃小猛
清華大學(xué) 地球系統(tǒng)科學(xué)系,北京100084
摘要: 球面質(zhì)心Voronoi網(wǎng)格(SCVT)是一種高質(zhì)量的非結(jié)構(gòu)網(wǎng)格,,被國(guó)內(nèi)外知名地球系統(tǒng)模式所采用,。國(guó)際上,已有開(kāi)源項(xiàng)目Message Passing Interface SCVT(MPI-SCVT)實(shí)現(xiàn)了并行的SCVT生成,。然而,,盡管MPI-SCVT可以很好地適用于一般分辨率網(wǎng)格的生成,當(dāng)所需網(wǎng)格的分辨率非常高時(shí),,MPI-SCVT的使用會(huì)出現(xiàn)多個(gè)問(wèn)題,,包括初始網(wǎng)格點(diǎn)質(zhì)量差、大數(shù)據(jù)MPI通信,、外部庫(kù)調(diào)用以及I/O問(wèn)題,。對(duì)于這些問(wèn)題,提出了一整套解決方案,。實(shí)踐表明,,應(yīng)用此方案可以順利完成全球1.9 km分辨率網(wǎng)格的生成,且到達(dá)相同精度時(shí)所需迭代步數(shù)顯著減少,,節(jié)約了計(jì)算時(shí)間,。
中圖分類號(hào): TP311
文獻(xiàn)標(biāo)識(shí)碼: A
DOI:10.16157/j.issn.0258-7998.222602
中文引用格式: 劉壯,黃小猛. 高分辨率全球非結(jié)構(gòu)網(wǎng)格生成實(shí)踐[J].電子技術(shù)應(yīng)用,,2022,,48(6):103-106,111.
英文引用格式: Liu Zhuang,,Huang Xiaomeng. Generating high-resolution global unstructured meshes[J]. Application of Electronic Technique,,2022,48(6):103-106,,111.
Generating high-resolution global unstructured meshes
Liu Zhuang,,Huang Xiaomeng
Department of Earth System Science,Tsinghua University,,Beijing 100084,,China
Abstract: The Spherical Centroid Voronoi tessellations(SCVT) are a kind of high-quality unstructured meshes, which are adopted by well-known earth system models at home and abroad. Internationally, the open source project Message Passing Interface SCVT(MPI-SCVT) has realized the parallel SCVT generation. However, although MPI-SCVT works well for the generation of general-resolution meshes, the use of MPI-SCVT presents several problems when the required mesh is of very high resolution, including the poor quality of initial mesh points, large data MPI communication problems, external library calling problems and I/O problems. For these problems, a set of solutions are proposed. Practice shows that the application of these solutions can successfully complete the generation of the global 1.9 km resolution grid, and the number of iterations is significantly reduced when reaching the same accuracy, which saves the calculation time.
Key words : generation of unstructured meshes,;centroid Voronoi tessellations;high resolution,;iteration optimization

0 引言

    近年來(lái),,隨著計(jì)算機(jī)計(jì)算能力的提升與數(shù)值方法的發(fā)展,非結(jié)構(gòu)網(wǎng)格在地球系統(tǒng)模式中得到了越來(lái)越多的應(yīng)用[1-2],。不同于結(jié)構(gòu)網(wǎng)格,,非結(jié)構(gòu)網(wǎng)格沒(méi)有極點(diǎn)附近網(wǎng)格收縮而出現(xiàn)奇異的問(wèn)題;同時(shí),,非結(jié)構(gòu)網(wǎng)格可以更靈活地處理各種邊界條件,、實(shí)現(xiàn)局部網(wǎng)格加密等。

在各種非結(jié)構(gòu)網(wǎng)格中,,球面質(zhì)心Voronoi網(wǎng)格[3](Spherical Centroid Voronoi Tessellations,SCVT)因具備良好的性質(zhì)而得到廣泛應(yīng)用,。生成SCVT一般采用的Lloyd算法[3]是一個(gè)不動(dòng)點(diǎn)迭代算法,,其計(jì)算量與生成的網(wǎng)格點(diǎn)數(shù)成正比。為應(yīng)對(duì)快速生成高分辨率SCVT的挑戰(zhàn),,Jacobsen等[4]提出了基于區(qū)域分解和球極投影的并行算法,,并在GitHub開(kāi)源了其代碼(MPI-SCVT:https://github.com/douglasjacobsen/MPI-SCVT)。數(shù)值實(shí)驗(yàn)顯示了MPI-SCVT相對(duì)于串行算法的加速效果,。

    盡管MPI-SCVT可以很好地適用于一般分辨率下SCVT的生成,,當(dāng)所需網(wǎng)格的分辨率非常高(例如2 km以下)時(shí),MPI-SCVT的使用會(huì)出現(xiàn)一系列問(wèn)題,。首先,,MPI-SCVT內(nèi)置的幾種網(wǎng)格初始化方法生成的網(wǎng)格點(diǎn)質(zhì)量較差,與最終的收斂結(jié)果距離較遠(yuǎn),,這使得迭代步數(shù)過(guò)多,,程序整體運(yùn)行時(shí)間長(zhǎng)。其次,,高分辨率導(dǎo)致迭代過(guò)程中通信的數(shù)據(jù)量大,,MPI-SCVT使用的boost MPI(http://www.boost.org)單次通信數(shù)據(jù)量超過(guò)一定大小(約2 GB)時(shí)會(huì)出錯(cuò)。再者,,MPI-SCVT調(diào)用外部庫(kù)Triangle[5]實(shí)現(xiàn)平面Delaunay三角網(wǎng)格[4]的構(gòu)建,,當(dāng)單次輸入網(wǎng)格點(diǎn)數(shù)超過(guò)約42 600 000時(shí),Triangle無(wú)法正常運(yùn)行,。最后,,高分辨率導(dǎo)致輸出變量較大,使用外部庫(kù)NetCDF-CXX無(wú)法完成所需NetCDF文件的輸出,。




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作者信息:

劉  壯,,黃小猛

(清華大學(xué) 地球系統(tǒng)科學(xué)系,北京100084)

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