A finite element alternative to infinite elements

Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil–structure interaction in a layered half-space

“…OWWEs, high-order local absorbing boundary conditions, CFABCs, have been developed [15][16][17][18][19][20]. Following is an overview of the derivation of the OWWE and CFABC.…”

“…Guddati [14] developed arbitrary wide-angle wave equations (AWWEs) applicable for general heterogeneous, anisotropic, porous, viscoelastic media and showed that the AWWEs are equivalent to the continued fraction approximation. The CFABCs have been applied successfully to problems of scalar wave propagation [15], dispersive acoustic wave propagation [16], elastic wave propagation [17], statics [18], and wave propagation in anisotropic media [19,20]. It has been shown that the CFABCs are arbitrarily high-order local absorbing boundary conditions that are effective in modeling wave propagation in various unbounded domains.…”

A domain decomposition method for concurrent coupling of multiscale models

“…Although there exist many approaches to approximate DtN map of half-space/unbounded domains, we choose the method perfectly matched discrete layers (PMDL) [14] adapted for elliptic problems [18]. Given in the following text is a brief summary of PMDL.…”

“…As indicated in Figure B.1(b), when the half-space is replaced by a standard linear FE C another half-space and the DtN map of the resulting composite half-space is no longer identical to that of the original half-space (because of discretization errors), the main idea behind PMDL is the fact that when midpoint-integrated linear FEs are used to discretize the half-space, then the DtN map of the discretized system is identical to the continuous half-space stiffness. As seen in Figure B.1(c), when the half-space is replaced by a midpoint-integrated linear FE attached to another half-space, then the resulting composite half-space has the same DtN map as the original half-space (see [18] for details). This process of discretizing the half-space can be carried out recursively to fully discretize the half-space, and this assembly of midpoint-integrated FE is referred to as PMDL.…”

“…where L i are the lengths of the midpoint-integrated FE that can be chosen to minimize the error in the DtN approximation and are the parameters of PMDL ( Figure B.1(e)). The reader is referred to [18] for a discussion on the choice of element lengths and extension to higher dimensions. Equation (B.3) can be viewed as approximating the exact DtN map (K 1 ) by the PMDL operator (S pmdl n ) and can be written in a block form as…”