A hierarchical vector basisfunctions based discontinuous Galerkin Time Domain (DGTD) method with Conformal Perfect Matching Layer (CPML) is proposed to analyze electromagnetic scattering problems. The total field/sca...
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ISBN:
(纸本)9781665432436
A hierarchical vector basisfunctions based discontinuous Galerkin Time Domain (DGTD) method with Conformal Perfect Matching Layer (CPML) is proposed to analyze electromagnetic scattering problems. The total field/scattered field (TF/SF) technology for generating plane wave is further studied. By unifying the TF/SF boundary and the PML boundary, the construction and subdivision of the computational domain as well as the memory space required for calculation are simplified. In addition, the total degree of freedom (DoF) is reduced while maintaining the calculation accuracy by using hierarchical basis functions of different orders to expand the electric and magnetic components. The effectiveness of the new technology implemented is validated by two numerical cases.
A high order vector finite element method to analyze the scattering of complex structure is considered. The solution of large sparse complex linear system equation is the most memory and time consuming part of the fin...
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ISBN:
(纸本)9781728131238
A high order vector finite element method to analyze the scattering of complex structure is considered. The solution of large sparse complex linear system equation is the most memory and time consuming part of the finite element method (FEM). In order to solve the scattering problems by FEM efficiently, we use Krylov subspace iterative method to solve the FEM matrix and further introduce the p -type multigrid preconditioning method as the preconditioner of the iterative method. Finally, some numerical examples are presented to show the reliability and efficiency of the method in this paper.
A 2-D discontinuous Galerkin time-domain (DGTD) scheme based on high-order hierarchical basis function is presented in this paper. Combined with the shift operator method solving the electromagnetic problem of dispers...
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A 2-D discontinuous Galerkin time-domain (DGTD) scheme based on high-order hierarchical basis function is presented in this paper. Combined with the shift operator method solving the electromagnetic problem of dispersive media in finite-difference time domain, the iterative formula of DGTD method in dealing with plasma media is given. On this basis, taking the example of line element radiation, the computing ability of different basisfunctions is compared. To study the transmission characteristics of the electromagnetic (EM) wave in sheath, the DGTD calculation models of the plasma sheath of a blunt cone at different flight heights and velocities are established using Lagrange interpolation technique based on the calculation results of COMSOL (business software). The influences of antenna position, flight altitude, and flight speed on transmission characteristics of the EM wave are discussed through calculation and analyses.
The numerical modeling of the advanced electromagnetic well-logging problems is very challenging because it requires tremendous workload of grid meshing and computation. For example, global meshing and simulation have...
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The numerical modeling of the advanced electromagnetic well-logging problems is very challenging because it requires tremendous workload of grid meshing and computation. For example, global meshing and simulation have to be done repeatedly for every logging position, because the model includes complex sensor arrays moving continuously along the borehole. In this paper, an efficient nonconformal finite element domain decomposition method is developed to solve these problems efficiently. First, the well-logging model is divided into two nonconformal subdomains so that the sensing arrays inside the borehole are separated from the beds outside. Since the mesh size between different subdomains can be inconsistent, well-logging modeling can significantly reduce the unknowns and computational cost. Second, a second-order transmission condition is implemented successfully in a quasi-symmetrical form via a novel treatment of Gaussian integration on the nonconformal interface. Finally, a hierarchical hexahedral basisfunction is introduced to further reduce the unknowns and extend the applicability of the method to multiscale problems. Numerical examples show that this method greatly reduces the memory cost and speeds up the computation compared with the traditional finite element method, especially when the response needs to be simulated repeatedly while the logging tools keep moving along the borehole.
A new set of higher order hierarchical basis functions is proposed for expansion of the current in electrical field integral equations (EFIE) solved by multilevel fast multipole algorithm (MLFMA) for the cavity scatte...
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ISBN:
(纸本)9781424418794
A new set of higher order hierarchical basis functions is proposed for expansion of the current in electrical field integral equations (EFIE) solved by multilevel fast multipole algorithm (MLFMA) for the cavity scattering problem. The hierarchical two-level spectral preconditioning technique is developed to solve EFIE with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The sparse approximate inverse (SAI) preconditioner based on the higher order hierarchical basis functions is used to damp the high frequencies of the error and the low frequencies is eliminated by a spectral preconditioner in a two-level manner defined on the lower order basisfunctions. The spectral preconditioner is combined with SAI preconditioner to obtain a hierarchical two-level spectral preconditioner. This newly constructed hierarchical two-level spectral preconditioner is used to speed up the restarted GMRES iterative algorithm. Numerical experiments indicate that the new preconditioner is efficient for the MLFMA and can significantly reduce both the iteration number and computational time.
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