The Boundary Element Method for the Helmholtz Equation ... - FEI VÅ B

8540.540.430.430.220.320100.20.110−0.2−10−0.1−1−0.4−2−0.2−2−0.6−3−0.3−3−0.8−4−4−2024024(a) Real part.−2−4−0.4−0.5−4−4−202024 4(b) Imaginary part.−2−4−1Figure 5.11: Scattered wave on the sound-hard cube with E = 1200.4413130.52210.51000−10−1−0.5−2−2−3−0.5−3−1−4−4−2024024(a) Real part.−2−4−1−4−4−202024 4(b) Imaginary part.−2−4−1.5Figure 5.12: Total wave on the sound-hard cube with E = 1200.5.6 Exterior Mixed Boundary Value ProblemFinally, we consider the exterior mixed boundary value problem (3.53) with κ = 2, thetesting solution (5.7) and Ω being the sphere and the cube. The testing domains aredecomposed in the same way as in the case of the interior mixed problem in Section 5.3.We solve the problem of finding the missing Cauchy data using the discretized Galerkinequations corresponding to the symmetric approach (3.56), i.e.,a(s h , t h , ψ k , ϕ l ) = F (ψ k , ϕ l )for all k ∈ E D , j ∈ N N