Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of p...Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.展开更多
The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) appr...The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.展开更多
When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly M...When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,展开更多
文摘Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.
基金Project(41174061) supported by the National Natural Science Foundation of ChinaProject(2011QNZT011) supported by the Free Exploration Program of Central South University,China
文摘The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.
基金supported jointly by the 973 Program (Grant No.2007CB209505)the National Natural Science Fund (Grant No.40704019,40674061)+1 种基金the School Basic Research Fund of Tsinghua University (JC2007030)PetroChina Innovation Fund (Grant No.060511-1-1)
文摘When modeling wave propagation in infinite space, it is necessary to have stable absorbing boundaries to effectively eliminate spurious reflections from the truncation boundaries. The SH wave equations for Perfectly Matched Layers （PML） are deduced and their Crank-Nicolson scheme are presented in this paper. We use the second-, sixth-, and tenth-order finite difference and pseudo-spectral algorithms to compute the spatial derivatives. Two numerical models, a homogeneous isotropic medium and a multi-layer model with a cave, are designed to investigate how the absorbing boundary width and the algorithms determine PML effects. Numerical results show that, for PML, the low-order finite difference algorithms have fairly good absorbing effects when the absorbing boundary is thin, whereas, high-order algorithms always have good absorption when the boundary is thick. Finally, we discuss the reflection coefficient and point out its shortcomings, which is why we use the SNR to quantitatively scale the PML effects,
