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

86 5 Numerical Experimentswith the related system of linear equationsVκ,h −K κ,h s −¯V κ,h − 1 ¯M 2 h + ¯K κ,h gN=D κ,h t ¯M T h − ¯KT κ,h−¯D κ,h g D .K T κ,h− 1 2E N Err D Err D,p Err N Err N,p Err ϑ320 162 1.04 · 10 −2 6.32 · 10 −3 8.09 · 10 −1 7.75 · 10 −1 7.18 · 10 −21240 622 2.51 · 10 −3 1.74 · 10 −3 5.06 · 10 −1 4.54 · 10 −1 1.20 · 10 −27432 3718 4.16 · 10 −4 2.68 · 10 −4 1.73 · 10 −1 1.53 · 10 −1 4.95 · 10 −4Table 5.15: Exterior mixed BVP on the sphere.E N Err D Err D,p Err N Err N,p Err ϑ300 152 2.76 · 10 −1 2.59 · 10 −1 1.71 · 10 −1 1.13 · 10 −1 1.24 · 10 −11200 602 1.01 · 10 −1 4.68 · 10 −2 6.52 · 10 −2 5.71 · 10 −2 7.78 · 10 −27500 3752 2.08 · 10 −2 1.31 · 10 −2 2.41 · 10 −2 2.29 · 10 −2 1.11 · 10 −2Table 5.16: Exterior mixed BVP on the cube.The results are summarized in Tables 5.15, 5.16 with the errors given by (5.6) and thecurve ϑ: [0, 1] → R 3 defined by (5.9).