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

78 5 Numerical Experimentsand the matrix formulationD κ,h g D = 12 MT h − KT κ,hg N .E N Err D Err D,p Err ϑ320 162 5.33 · 10 −2 1.82 · 10 −2 4.96 · 10 −21240 622 1.55 · 10 −2 4.94 · 10 −3 1.41 · 10 −27432 3718 2.75 · 10 −3 7.45 · 10 −4 2.72 · 10 −3Table 5.4: Interior Neumann BVP on the sphere.E N Err D Err D,p Err ϑ300 152 8.11 · 10 −2 3.96 · 10 −2 4.45 · 10 −21200 602 1.79 · 10 −2 8.95 · 10 −3 1.04 · 10 −27500 3752 2.63 · 10 −3 1.36 · 10 −3 1.62 · 10 −3Table 5.5: Interior Neumann BVP on the cube.E N Err D Err D,p Err ϑ3962 1983 1.11 · 10 −1 5.89 · 10 −3 9.44 · 10 −27510 3757 9.71 · 10 −2 2.41 · 10 −3 8.31 · 10 −2Table 5.6: Interior Neumann BVP on the elephant.120012000.81500.81500.60.41000.60.41000.2500.2500−0.200−0.20−0.4−50−0.4−50−0.6−0.8−100−0.6−0.8−100−1−1−0.500.500.51 1(a) Real part.−0.5−1−150−200−1−1−0.500.500.51 1(b) Imaginary part.−0.5−1−150−200Figure 5.4: Solution to the interior Neumann BVP on the cube with E = 7500.