本文主要研究内容
作者邱长凯（2019）在《基于有理Krylov和代数多重网格的三维主动源电磁法矢量有限元正演研究》一文中研究指出：近十年来,随着对深地和深海资源勘查的迫切需要,传统的地面电磁法、采用移动平台搭载的航空电磁法和海洋电磁法都进入快速发展时期,在矿产勘探、油气勘探、水文地质勘探和环境地球物理勘探等领域发挥越来越重要的作用。电磁勘探数据的精细解释离不开完备的三维正反演理论和可靠的三维正反演技术。现有的数值模拟手段针对特定的电磁勘探方法需要开发特定的算法,不具有通用性。采用规则网格的数值模拟方法无法精确刻画地形、起伏界面和复杂异常体等。采用直接求解器的数值模拟方法由于内存消耗巨大,无法满足较大规模三维反演的需要。攻克上述理论瓶颈和技术难题将为三维电磁数据处理解释工作提供一定的理论支持,为三维电磁数据反演打下坚实的基础。为了解决上述问题,本文致力于系统研究使用非结构四面体网格和矢量有限元求解频率域或时间域主动源电磁正演模拟问题。首先从Maxwell方程组出发,推导总电场满足的偏微分方程和边界条件;其次使用电偶极子近似任意电性或磁性发射源,统一主动源电磁矢量有限元正演模拟理论;进而采用非结构四面体网格刻画任意复杂的地电模型,使用切向分量连续且单元内无散的一阶Nédélec矢量基函数近似单元内的电场分布,完成空间离散;随后由电势满足的Possion方程,使用标量有限元求解电性源时间域电磁法的初值电场。在标量或矢量有限元方程推导中,均由Galerkin加权余量法得到线性代数方程组。对于频率域电磁模拟,得到关于电场和频率的大型复线性代数方程组;对于时间域电磁模拟,使用无条件稳定的二阶向后欧拉方法进行时间离散,得到关于电场和时间步长的大型实线性代数方程组。为了验证总场方法的准确性和可靠性,研究基于直接求解方法的三维时间域和频率域电磁法正演模拟技术。采用稀疏并行多波前直接求解器MUMPS执行LU分解,求解得到电场解向量,进而插值出任意点的电磁场值。将本文的算法应用于四种偶极子场源的正演模拟,说明基于总场的有限元离散方法的通用性。为了提高时间域电磁法的正演模拟速度,研究求解时间域电磁问题的有理Krylov方法。由矢量有限元离散的一阶电场偏微分方程,直接得到矩阵指数函数和向量乘积表示的电场解向量,无需任何时间步长离散。提出加权偏移参数优化方法,减少有理Arnoldi算法的迭代次数以提高计算速度。使用有理Arnoldi算法构建有理Krylov子空间正交基,从而由正交基函数计算任意时刻的电场解向量。以时间域航空电磁和时间域海洋可控源电磁为例说明有理Krylov方法的准确性,分析了典型地电模型的响应,并比较了和向后欧拉方法的计算效率。鉴于直接求解算法内存消耗巨大,可扩展性较差,不适合求解较大规模的电磁模拟问题,进一步研究预条件迭代求解时间域电场方程。在每个时间步长,使用二阶向后欧拉离散得到关于电场的线性代数方程组,本质上是求解实系数Maxwell方程。基于Hiptmair-Xu分解构造H(curl)空间的三个附属空间,并引入高效的代数多重网格预条件子,从而使用共轭梯度求解器迭代求解有限元离散方程。以典型的地面瞬变电磁和时间域海洋可控源电磁模型为例,研究了空气电导率和时间步长对共轭梯度迭代求解器鲁棒性的影响,并分析了初值优化技术对计算效率的提升。最后研究频率域电场双旋度方程的预条件迭代求解方法。将复电场方程转换为等效的实形式,引入对称的块对角矩阵预条件线性代数方程组,将预条件问题转换为求解实系数的Maxwell方程,探究预条件后线性代数方程组的条件数。在外层迭代,使用可变预条件的广义最小残差法迭代求解实线性代数方程组(未知数个数为2N);在内层迭代,使用代数多重网格预条件共轭梯度法迭代求解预条件问题(未知数个数为N)。以全空间、半空间磁偶极子源和地面短导线源为例研究迭代求解器对于常系数和变系数Maxwell方程的可行性;针对频率域海洋可控源电磁模型,详细研究空气电导率和频率对迭代求解器鲁棒性的影响,并统计不同未知数规模时迭代求解器的内存消耗。基于上述理论,本文通过大量模型算例证明提出的总场算法准确度高,可靠性和通用性均较好。对于时间域电磁模拟问题,基于加权偏移参数优化策略,单向量有理Krylov方法和block有理Krylov方法均具有很高的计算精度;由于有理Krylov方法只需求解40次线性代数方程组,比向后欧拉方法快7至13倍;由于block有理Krylov方法浮点数计算效率更高,更好地利用了缓存,对于中等数目的多源电磁模拟问题比单向量有理Krylov方法快1.26到1.48倍。时间域电磁法多重网格预条件迭代求解表明,空气电导率和时间步长基本不影响共轭梯度求解器的收敛速度,采用初值优化后计算效率能够提升约17%到34%。对于频率域电磁模拟问题,附属空间预条件广义最小残差求解器只需几十次即可收敛;对于海洋可控源电磁问题,预条件迭代算法的鲁棒性非常好,不受空气电导率和频率的影响;得益于代数多重网格预条件子和重启的广义最小残差求解器优异的内存表现,本文成功在普通个人工作站上求解约2500万实未知数的三维频率域电磁模拟问题,表明代数多重网格预条件迭代求解器对于大规模电磁问题具有巨大的潜力。
Abstract
jin shi nian lai ,sui zhao dui shen de he shen hai zi yuan kan cha de pai qie xu yao ,chuan tong de de mian dian ci fa 、cai yong yi dong ping tai da zai de hang kong dian ci fa he hai xiang dian ci fa dou jin ru kuai su fa zhan shi ji ,zai kuang chan kan tan 、you qi kan tan 、shui wen de zhi kan tan he huan jing de qiu wu li kan tan deng ling yu fa hui yue lai yue chong yao de zuo yong 。dian ci kan tan shu ju de jing xi jie shi li bu kai wan bei de san wei zheng fan yan li lun he ke kao de san wei zheng fan yan ji shu 。xian you de shu zhi mo ni shou duan zhen dui te ding de dian ci kan tan fang fa xu yao kai fa te ding de suan fa ,bu ju you tong yong xing 。cai yong gui ze wang ge de shu zhi mo ni fang fa mo fa jing que ke hua de xing 、qi fu jie mian he fu za yi chang ti deng 。cai yong zhi jie qiu jie qi de shu zhi mo ni fang fa you yu nei cun xiao hao ju da ,mo fa man zu jiao da gui mo san wei fan yan de xu yao 。gong ke shang shu li lun ping geng he ji shu nan ti jiang wei san wei dian ci shu ju chu li jie shi gong zuo di gong yi ding de li lun zhi chi ,wei san wei dian ci shu ju fan yan da xia jian shi de ji chu 。wei le jie jue shang shu wen ti ,ben wen zhi li yu ji tong yan jiu shi yong fei jie gou si mian ti wang ge he shi liang you xian yuan qiu jie pin lv yu huo shi jian yu zhu dong yuan dian ci zheng yan mo ni wen ti 。shou xian cong Maxwellfang cheng zu chu fa ,tui dao zong dian chang man zu de pian wei fen fang cheng he bian jie tiao jian ;ji ci shi yong dian ou ji zi jin shi ren yi dian xing huo ci xing fa she yuan ,tong yi zhu dong yuan dian ci shi liang you xian yuan zheng yan mo ni li lun ;jin er cai yong fei jie gou si mian ti wang ge ke hua ren yi fu za de de dian mo xing ,shi yong qie xiang fen liang lian xu ju chan yuan nei mo san de yi jie Nédélecshi liang ji han shu jin shi chan yuan nei de dian chang fen bu ,wan cheng kong jian li san ;sui hou you dian shi man zu de Possionfang cheng ,shi yong biao liang you xian yuan qiu jie dian xing yuan shi jian yu dian ci fa de chu zhi dian chang 。zai biao liang huo shi liang you xian yuan fang cheng tui dao zhong ,jun you Galerkinjia quan yu liang fa de dao xian xing dai shu fang cheng zu 。dui yu pin lv yu dian ci mo ni ,de dao guan yu dian chang he pin lv de da xing fu xian xing dai shu fang cheng zu ;dui yu shi jian yu dian ci mo ni ,shi yong mo tiao jian wen ding de er jie xiang hou ou la fang fa jin hang shi jian li san ,de dao guan yu dian chang he shi jian bu chang de da xing shi xian xing dai shu fang cheng zu 。wei le yan zheng zong chang fang fa de zhun que xing he ke kao xing ,yan jiu ji yu zhi jie qiu jie fang fa de san wei shi jian yu he pin lv yu dian ci fa zheng yan mo ni ji shu 。cai yong xi shu bing hang duo bo qian zhi jie qiu jie qi MUMPSzhi hang LUfen jie ,qiu jie de dao dian chang jie xiang liang ,jin er cha zhi chu ren yi dian de dian ci chang zhi 。jiang ben wen de suan fa ying yong yu si chong ou ji zi chang yuan de zheng yan mo ni ,shui ming ji yu zong chang de you xian yuan li san fang fa de tong yong xing 。wei le di gao shi jian yu dian ci fa de zheng yan mo ni su du ,yan jiu qiu jie shi jian yu dian ci wen ti de you li Krylovfang fa 。you shi liang you xian yuan li san de yi jie dian chang pian wei fen fang cheng ,zhi jie de dao ju zhen zhi shu han shu he xiang liang cheng ji biao shi de dian chang jie xiang liang ,mo xu ren he shi jian bu chang li san 。di chu jia quan pian yi can shu you hua fang fa ,jian shao you li Arnoldisuan fa de die dai ci shu yi di gao ji suan su du 。shi yong you li Arnoldisuan fa gou jian you li Krylovzi kong jian zheng jiao ji ,cong er you zheng jiao ji han shu ji suan ren yi shi ke de dian chang jie xiang liang 。yi shi jian yu hang kong dian ci he shi jian yu hai xiang ke kong yuan dian ci wei li shui ming you li Krylovfang fa de zhun que xing ,fen xi le dian xing de dian mo xing de xiang ying ,bing bi jiao le he xiang hou ou la fang fa de ji suan xiao lv 。jian yu zhi jie qiu jie suan fa nei cun xiao hao ju da ,ke kuo zhan xing jiao cha ,bu kuo ge qiu jie jiao da gui mo de dian ci mo ni wen ti ,jin yi bu yan jiu yu tiao jian die dai qiu jie shi jian yu dian chang fang cheng 。zai mei ge shi jian bu chang ,shi yong er jie xiang hou ou la li san de dao guan yu dian chang de xian xing dai shu fang cheng zu ,ben zhi shang shi qiu jie shi ji shu Maxwellfang cheng 。ji yu Hiptmair-Xufen jie gou zao H(curl)kong jian de san ge fu shu kong jian ,bing yin ru gao xiao de dai shu duo chong wang ge yu tiao jian zi ,cong er shi yong gong e ti du qiu jie qi die dai qiu jie you xian yuan li san fang cheng 。yi dian xing de de mian shun bian dian ci he shi jian yu hai xiang ke kong yuan dian ci mo xing wei li ,yan jiu le kong qi dian dao lv he shi jian bu chang dui gong e ti du die dai qiu jie qi lu bang xing de ying xiang ,bing fen xi le chu zhi you hua ji shu dui ji suan xiao lv de di sheng 。zui hou yan jiu pin lv yu dian chang shuang xuan du fang cheng de yu tiao jian die dai qiu jie fang fa 。jiang fu dian chang fang cheng zhuai huan wei deng xiao de shi xing shi ,yin ru dui chen de kuai dui jiao ju zhen yu tiao jian xian xing dai shu fang cheng zu ,jiang yu tiao jian wen ti zhuai huan wei qiu jie shi ji shu de Maxwellfang cheng ,tan jiu yu tiao jian hou xian xing dai shu fang cheng zu de tiao jian shu 。zai wai ceng die dai ,shi yong ke bian yu tiao jian de an yi zui xiao can cha fa die dai qiu jie shi xian xing dai shu fang cheng zu (wei zhi shu ge shu wei 2N);zai nei ceng die dai ,shi yong dai shu duo chong wang ge yu tiao jian gong e ti du fa die dai qiu jie yu tiao jian wen ti (wei zhi shu ge shu wei N)。yi quan kong jian 、ban kong jian ci ou ji zi yuan he de mian duan dao xian yuan wei li yan jiu die dai qiu jie qi dui yu chang ji shu he bian ji shu Maxwellfang cheng de ke hang xing ;zhen dui pin lv yu hai xiang ke kong yuan dian ci mo xing ,xiang xi yan jiu kong qi dian dao lv he pin lv dui die dai qiu jie qi lu bang xing de ying xiang ,bing tong ji bu tong wei zhi shu gui mo shi die dai qiu jie qi de nei cun xiao hao 。ji yu shang shu li lun ,ben wen tong guo da liang mo xing suan li zheng ming di chu de zong chang suan fa zhun que du gao ,ke kao xing he tong yong xing jun jiao hao 。dui yu shi jian yu dian ci mo ni wen ti ,ji yu jia quan pian yi can shu you hua ce lve ,chan xiang liang you li Krylovfang fa he blockyou li Krylovfang fa jun ju you hen gao de ji suan jing du ;you yu you li Krylovfang fa zhi xu qiu jie 40ci xian xing dai shu fang cheng zu ,bi xiang hou ou la fang fa kuai 7zhi 13bei ;you yu blockyou li Krylovfang fa fu dian shu ji suan xiao lv geng gao ,geng hao de li yong le huan cun ,dui yu zhong deng shu mu de duo yuan dian ci mo ni wen ti bi chan xiang liang you li Krylovfang fa kuai 1.26dao 1.48bei 。shi jian yu dian ci fa duo chong wang ge yu tiao jian die dai qiu jie biao ming ,kong qi dian dao lv he shi jian bu chang ji ben bu ying xiang gong e ti du qiu jie qi de shou lian su du ,cai yong chu zhi you hua hou ji suan xiao lv neng gou di sheng yao 17%dao 34%。dui yu pin lv yu dian ci mo ni wen ti ,fu shu kong jian yu tiao jian an yi zui xiao can cha qiu jie qi zhi xu ji shi ci ji ke shou lian ;dui yu hai xiang ke kong yuan dian ci wen ti ,yu tiao jian die dai suan fa de lu bang xing fei chang hao ,bu shou kong qi dian dao lv he pin lv de ying xiang ;de yi yu dai shu duo chong wang ge yu tiao jian zi he chong qi de an yi zui xiao can cha qiu jie qi you yi de nei cun biao xian ,ben wen cheng gong zai pu tong ge ren gong zuo zhan shang qiu jie yao 2500mo shi wei zhi shu de san wei pin lv yu dian ci mo ni wen ti ,biao ming dai shu duo chong wang ge yu tiao jian die dai qiu jie qi dui yu da gui mo dian ci wen ti ju you ju da de qian li 。
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论文作者分别是来自吉林大学的邱长凯，发表于刊物吉林大学2019-06-25论文，是一篇关于地球物理电磁勘探论文,可控源电磁法论文,矢量有限元论文,三维正演论文,有理论文,代数多重网格论文,直接求解论文,向后欧拉离散论文,吉林大学2019-06-25论文的文章。本文可供学术参考使用，各位学者可以免费参考阅读下载，文章观点不代表本站观点，资料来自吉林大学2019-06-25论文网站，若本站收录的文献无意侵犯了您的著作版权，请联系我们删除。
标签：地球物理电磁勘探论文; 可控源电磁法论文; 矢量有限元论文; 三维正演论文; 有理论文; 代数多重网格论文; 直接求解论文; 向后欧拉离散论文; 吉林大学2019-06-25论文;