Helmholtz传输输特征值问题的高效计算方法

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1、学校代码:10663学号:5141000010贵贵贵州州州师师师范范范大大大学学学博博博士士士学学学位位位论论论文文文Helmholtz传传传输输输特特特征征征值值值问问问题题题的的的高高高效效效计计计算算算方方方法法法EfficientComputationalMethodsfortheHelmholtzTransmissionEigenvalueProblem专业名称：计算数学专业代码：070102研究方向：有限元申请人姓名：韩家宇导师姓名：杨一都(教授)二零一八年四月八日原创性声明本人郑重声明:所呈交的学位论文,是本人在导师的悉心指导下,独立进行研究所取得的成

2、果.除文中已经注明引用的内容外,本论文不包含任何其他个人或集体已经发表或撰写过的科研成果.对本文的研究在做出重要贡献的个人或集体,均已在文中以明确方式标明.本人完全意识到本声明的法律责任由本人承担.论文作者签名：日期:年月日关于学位论文使用授权的声明本人完全了解贵州师范大学有关保留、使用学位论文的规定、同意学校保留或向国家有关部门或机构送交论文的复印件和电子版,允许论文被查阅和借阅;本人授权贵州师范大学可以将本学位论文的全部或部分内容编入有关数据库进行检索,可以采用影印、缩印或其他复制手段保存论文和汇编学位论文.(保密论文在解密后应遵守此规定)论文作者签名：导师

3、签名：日期:年月日目录摘要······························································································IAbstract······························································································III第一章预备知识································································

4、·····················1第二章多网格方案··················································································82.1一个新的二网格方法······································································82.2数值试验·················································································

5、····14第三章自适应算法··················································································183.1后验误差估计···············································································183.2自适应算法和数值试验···································································303.2.1单位方形上的模型问

6、题··························································313.2.2L型区域上的模型问题···························································32第四章H2-协调谱元法·············································································384.1一个Hm-协调谱元法············································

7、··························384.2传输特征值H2-协调谱元逼近···························································454.3数值试验·····················································································474.4结论和进一步工作·········································································

8、47第五章非协调元方法·