Explicit finite element artificial boundary scheme for transient scalar waves in two‐dimensional unbounded waveguide

Abstract

SUMMARYTo simulate the transient scalar wave propagation in a two-dimensional unbounded waveguide, an explicit finite element artificial boundary scheme is proposed, which couples the standard dynamic finite element method for complex near field and a high-order accurate artificial boundary condition (ABC) for simple far field. An exact dynamic-stiffness ABC that is global in space and time is constructed. A temporal localization method is developed, which consists of the rational function approximation in the frequency domain and the auxiliary variable realization into time domain. This method is applied to the dynamicstiffness ABC to result in a high-order accurate ABC that is local in time but global in space. By discretizing the high-order accurate ABC along artificial boundary and coupling the result with the standard lumped-mass finite element equation of near field, a coupled dynamic equation is obtained, which is a symmetric system of purely second-order ordinary differential equations in time with the diagonal mass and non-diagonal damping matrices. A new explicit time integration algorithm in structural dynamics is used to solve this equation. Numerical examples are given to demonstrate the effectiveness of the proposed scheme.

Modification Research of the Internal Substructure Method for Seismic Wave Input in Deep Underground Structure‐Soil Systems

“…erefore they participate in the calculation of equivalent seismic loads, and thus the restrictions on the applied artificial boundaries are more severe in BSM. Namely, they need to be the stress-type boundary conditions (such as the viscous boundaries [16] and the viscoelastic boundaries [17,18]), while the displacement-type artificial boundaries such as transmitting boundaries [14,15] or the perfectly matched layers [12,13] are not applicable in BSM. e original and modified ISMs avoid the participation of the artificial boundaries in the process of equivalent loads calculation by spatially separating the input of seismic waves and the absorption of scattered waves.…”

“…e representative achievements in the artificial boundaries include the boundary element method [9,10], the infinite element method [11], perfectly matched layers [12,13], transmitting boundaries [14,15], viscous boundaries [16], viscoelastic boundaries [17,18], and exact absorbing boundaries [19,20]. However, due to the application of the artificial boundaries, a new problem appears in inputting the seismic waves into the finite model without affecting the transmission of outgoing waves.…”

A local artificial‐boundary condition for simulating transient wave radiation in fluid‐saturated porous media of infinite domains

“…Normal stress boundary condition. The normal stress can be obtained by substituting Equations (22) into (30).…”

“…The advance on the artificial‐boundary conditions for the one‐phase medium is reviewed firstly as follows. The methods can be divided into two categories . The first category of methods involves the application of the global exact artificial‐boundary condition to the numerical models, such as the boundary element method , the thin‐layer method , the exact Kirchhoff integral method and the Dirichlet‐to‐Neumann method .…”

Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

“…Remarkable literature reviews on them are available in References [1][2][3][4][5]. These methods include the viscous boundary, 6 the viscous-spring boundary, [7][8][9][10] the extrapolation boundary, 11,12 the infinite element method, [13][14][15] the boundary element method, [16][17][18] the Engquist-Majda boundary, 19,20 Higdon boundary, 21,22 Bayliss-Turkel boundary 23,24 and their high-order local formulations, [25][26][27][28][29][30] the Dirichlet-to-Neumann (DtN) method 3,[31][32][33][34][35] and its temporally local formulations, [36][37][38][39][40][41] the consistent boundary (thin layer method) [42][43][44][45][46][47]…”