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《Chinese Journal of Geophysics》 2016-01
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Daubechies wavelet finite element method for solving the GPR wave equations

FENG De-Shan;YANG Bing-Kun;WANG Xun;DU Hua-Kun;School of Geosciences and Info-Physics,Central South University;Key Laboratory of Metallogenic Prediction of Non-Ferrous Metals and Geological Environment Monitor(Central South University) ,Ministry of Education;Fujian Academy of Building Research;Key Laboratory of Metallogenic Prediction of Non-Ferrous Metals and Geological Environment Monitor (Central South University),Ministry of Education;  
Based on the separable wavelet theory,we construct the two-dimensional Daubechies wavelet bases by means of one-dimensional Daubechies scaling functions,which is used for interpolation functions of solving the GPR wave equation,thus present the discrete format of twodimensional Daubechies wavelet finite element GPR equation.By introducing a transformation matrix,the transformation between the wavelet coefficient space and the GPR electromagnetic field is implemented.By introducing the degree of freedom condensation technique,it effectively solves the problem of too much freedom in internal wavelet unit during the solution process of the wavelet finite element,reducing the amount of calculation and can be coupled easily with traditional finite element method.Then the calculation formulas of connection coefficient used in Daubechies wavelet finite element are elaborated,which effectively resolve the difficulty and coreproblem in solving partial differential equations by wavelet finite element.Finally,with two typical GPR models as example,comparing the radar forward sections and the single waveforms between Daubechies wavelet finite element method and the traditional finite element method,and the result shows that under the conditions of the same dividing method and the number of nodes,the compact support and orthogonality of Daubechies wavelet finite element improves the solving efficiency to some extent,and it can be fitted well with the solving result of finite element method,validating the correctness of the Daubechies wavelet finite element method,which provides a new idea for solving the GPR wave equation.
【Fund】: 国家自然科学基金项目(41574116 41074085);; 中南大学创新驱动项目(2015CX008);中南大学升华育英人才计划;中南大学教师研究基金(2014JSJJ001);; 教育部新世纪优秀人才支持计划(NCET-12-0551);; 湖湘青年创新创业平台培养对象项目共同资助
【CateGory Index】: P631
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【Citations】
Chinese Journal Full-text Database 1 Hits
1 FENG De-Shan1,2,3,CHEN Cheng-Shen1,2,3,WANG Hong-Hua1,2,3 1 School of Geosciences and Info-Physics,Central South University,Changsha 410083,China 2 Key Laboratory of Metallogenic Prediction of Nonferrous Metals,Ministry of Education,Changsha 410083,China 3 Non-ferrous Resources and Geologic Disasters Prospecting Emphases Laboratory of Hunan,Changsha 410083,China;Finite element method GPR forward simulation based on mixed boundary condition[J];Chinese Journal of Geophysics;2012-11
【Co-citations】
Chinese Journal Full-text Database 6 Hits
1 YANG Feng-juan1,FAN Yun-ling1(Guangdong Institute of Geological Survey,Guangzhou 510080,China);An improved filter algorithm of direct arrive wave for GPR[J];Progress in Geophysics;2013-03
2 GAO Yi-Chao;XU Yan-Jie;JIN Feng;WANG Xiang;State Key Laboratory of Hydroscience and Hydraulic Engineering,Tsinghua University;Collage of Civil Engineering,Huaqiao University;Changjiang Institute of Survey Planning Design and Research;;The direct coupled model for dam-reservoir dynamic interaction analysis based on high-order doubly asymptotic open boundary[J];Chinese Journal of Geophysics;2013-12
3 FENG De-Shan;CHEN Jia-Wei;WU Qi;School of Geosciences and Info-Physics,Central South University;Department of Earth Science,Rice University;School of Earth and Space Sciences,Peking University;;A hybrid ADI-FDTD subgridding scheme for efficient GPR simulation of dispersion media[J];Chinese Journal of Geophysics;2014-04
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5 DU Liang;LIU Shu-cai;WANG Qi-ren;LIANG Qi-nian;GUO Wei-hong;ZHOU Xuan;China University of Mining &Technology;Hunan University of Science and Technology;Guangxi Bureau of Coal Geology;;Ground penetrating radar detecting saturation of plastic corrugated pipe grouting in prestressed deck[J];Progress in Geophysics;2014-06
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