The discretization of both kinds of variational equations, the type with DtN operator and the type with PML, follows the same scheme as applied for the semi-transparent Helmholtz equation in Section 8.1.
First, we discretize the computational domain. In the case of the formulation involving the DtN operator as transparent boundary condition, we just have to decompose the interval (0, L) into subintervals as in Section 8.1. In the case of the formulation with the PML as non-reflecting layer, we first have to truncate the semi-infinite exterior domains (see Figure 8.7), and second, we have to decompose the truncated domain into intervals. In both cases, we now step segment-wise through the computational domain (plus eventually ...
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