The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The co...The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.展开更多
Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two...Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.展开更多
Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting bo...Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.展开更多
The multi-transmitting formula (MTF) governed by a single artificial speed is analytically developed into a generalized MTF governed by a few artificial speeds to improve its capacity in simultaneous simulation of sev...The multi-transmitting formula (MTF) governed by a single artificial speed is analytically developed into a generalized MTF governed by a few artificial speeds to improve its capacity in simultaneous simulation of several one-way waves propagating at different speeds.The generalized MTF is then discretized and further generalized using the space extrapolation to improve its accuracies in numerical simulation of transient waves at large angles of incidence.The above two successive generalizitions of MTF based on the notion of normal transmission lead to a compact formula of local non-reflecting boundary condition.The formula not only provides a general representation of the major schemes of existing local boundary conditions but can be used to generate new schemes,which combine advantages of different schemes.展开更多
基金National Natural Science Foundation of China (50608024 and 50538050).
文摘The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.
基金the Key Projects in the National Science & Technology Pillar Program during the Twelfth Five-year Plan Period(Grant No.2015BAK17B01)Science Foundation of Institute of Engineering Mechanics,CEA under Grant No.2014B10+1 种基金Natural Science Foundation of Heilongjiang Province of China under Grant No.LC201403National Natural Science Foundation under Grant No.51378479 and No.51108431
文摘Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-freqaency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than x/2 times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.
基金the Joint Seismological Science Foundation. Prof. Dai Yishan in Harbin Engineering University has read the manuscript and made relevant comments The expansions of 1/r and r using the Legendre polynomials and the proof of eq (29) on the properties of
文摘Relationship between the radiation conditions at infinity and the transmitting boundary for numerical simulation of the near-field wave motion has been studied in this paper. The conclusion is that the transmitting boundary is approximately equivalent to the radiation conditions at infinity for a large class of infinite media. And the errors of the approximation are of the same order of magnitude as those of the finite elements or finite differences in numerical simulation of wave motion. This result provides a sound theoretical basis for the transmitting boundary used in the numerical simulation of the near-field wave motion and gives a complete explanation for the major experiences accumulated in applications of the transmitting boundary to the numerical simulation.
基金Project supported by the Joint Seismological Science Foundation.
文摘The multi-transmitting formula (MTF) governed by a single artificial speed is analytically developed into a generalized MTF governed by a few artificial speeds to improve its capacity in simultaneous simulation of several one-way waves propagating at different speeds.The generalized MTF is then discretized and further generalized using the space extrapolation to improve its accuracies in numerical simulation of transient waves at large angles of incidence.The above two successive generalizitions of MTF based on the notion of normal transmission lead to a compact formula of local non-reflecting boundary condition.The formula not only provides a general representation of the major schemes of existing local boundary conditions but can be used to generate new schemes,which combine advantages of different schemes.
