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postgraduate thesis: Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains
Title | Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains |
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Authors | |
Advisors | |
Issue Date | 2014 |
Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
Citation | Xu, B. [許博卿]. (2014). Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5351029 |
Abstract | A general convolutional version of perfectly matched layer (PML) formulation for second-order wave equations with displacement as the only unknown based on the coordinate stretching is proposed in this study, which overcomes the limitation of classical PML in splitting the displacement field and requires only minor modifications to existing finite element programs.
The first contribution concerns the development of a robust and efficient finite element program QUAD-CPML based on QUAD4M capable of simulating wave propagation in an unbounded domain. The more efficient hybrid-stress finite element was incorporated into the program to reduce the number of iterations for the equivalent linear dynamic analysis and the total time for the direct time integration. The incorporation of new element types was verified with the QUAD4M solutions to problems of dynamic soil response and the efficiency of hybrid-stress finite element was demonstrated compared to the classical finite elements.
The second development involves the implementation of a general convolutional perfectly matched layer (CPML) as an absorbing boundary condition for the modeling of the radiation of wave energy in an unbounded domain. The proposed non-split CPML formulation is displacement-based, which shows great compatibility with the direct time integration. This CPML formulation treats the convolutional terms as external forces and includes an updating scheme to calculate the temporal convolution terms arising from the Fourier transform. In addition, the performance of the CPML has been examined by various problems including a parametric study on a number of key coefficients that control the absorbing ability of the CPML boundary.
The final task of this thesis is to apply the developed CPML models to the dynamic analyses of soil-structure interaction (SSI) problems. Typical loading conditions including external load on the structure and underground wave excitation on the medium has been considered. Practical applications of CPML models include the numerical study on the effectiveness of the rubber-soil mixture (RSM) as an earthquake protection material and the report of vibrations induced by the passage of a high-speed train. The former investigates the effectiveness of the CPML models for the evaluation of the performance of RSM subject to seismic excitation and the latter tests the boundary effects on the accuracy of the results for train induced vibrations. Both studies show that CPML as an absorbing boundary condition is theoretically sound and effective for the analysis of soil-structure dynamic response. |
Degree | Doctor of Philosophy |
Subject | Seismic waves - Mathematical models Finite element method |
Dept/Program | Civil Engineering |
Persistent Identifier | http://hdl.handle.net/10722/208043 |
HKU Library Item ID | b5351029 |
DC Field | Value | Language |
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dc.contributor.advisor | Wong, N | - |
dc.contributor.advisor | Lo, SH | - |
dc.contributor.author | Xu, Boqing | - |
dc.contributor.author | 許博卿 | - |
dc.date.accessioned | 2015-02-06T14:19:36Z | - |
dc.date.available | 2015-02-06T14:19:36Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Xu, B. [許博卿]. (2014). Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5351029 | - |
dc.identifier.uri | http://hdl.handle.net/10722/208043 | - |
dc.description.abstract | A general convolutional version of perfectly matched layer (PML) formulation for second-order wave equations with displacement as the only unknown based on the coordinate stretching is proposed in this study, which overcomes the limitation of classical PML in splitting the displacement field and requires only minor modifications to existing finite element programs. The first contribution concerns the development of a robust and efficient finite element program QUAD-CPML based on QUAD4M capable of simulating wave propagation in an unbounded domain. The more efficient hybrid-stress finite element was incorporated into the program to reduce the number of iterations for the equivalent linear dynamic analysis and the total time for the direct time integration. The incorporation of new element types was verified with the QUAD4M solutions to problems of dynamic soil response and the efficiency of hybrid-stress finite element was demonstrated compared to the classical finite elements. The second development involves the implementation of a general convolutional perfectly matched layer (CPML) as an absorbing boundary condition for the modeling of the radiation of wave energy in an unbounded domain. The proposed non-split CPML formulation is displacement-based, which shows great compatibility with the direct time integration. This CPML formulation treats the convolutional terms as external forces and includes an updating scheme to calculate the temporal convolution terms arising from the Fourier transform. In addition, the performance of the CPML has been examined by various problems including a parametric study on a number of key coefficients that control the absorbing ability of the CPML boundary. The final task of this thesis is to apply the developed CPML models to the dynamic analyses of soil-structure interaction (SSI) problems. Typical loading conditions including external load on the structure and underground wave excitation on the medium has been considered. Practical applications of CPML models include the numerical study on the effectiveness of the rubber-soil mixture (RSM) as an earthquake protection material and the report of vibrations induced by the passage of a high-speed train. The former investigates the effectiveness of the CPML models for the evaluation of the performance of RSM subject to seismic excitation and the latter tests the boundary effects on the accuracy of the results for train induced vibrations. Both studies show that CPML as an absorbing boundary condition is theoretically sound and effective for the analysis of soil-structure dynamic response. | - |
dc.language | eng | - |
dc.publisher | The University of Hong Kong (Pokfulam, Hong Kong) | - |
dc.relation.ispartof | HKU Theses Online (HKUTO) | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works. | - |
dc.subject.lcsh | Seismic waves - Mathematical models | - |
dc.subject.lcsh | Finite element method | - |
dc.title | Convolutional perfectly matched layers for finite element modeling of wave propagation in unbounded domains | - |
dc.type | PG_Thesis | - |
dc.identifier.hkul | b5351029 | - |
dc.description.thesisname | Doctor of Philosophy | - |
dc.description.thesislevel | Doctoral | - |
dc.description.thesisdiscipline | Civil Engineering | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.5353/th_b5351029 | - |
dc.identifier.mmsid | 991040123029703414 | - |