Mechanical Quadrature Method and Splitting Extrapolation for Solving Dirichlet Boundary Integral Equation of Helmholtz Equation on Polygons

Table 1

The numerical results.

(𝑛1,𝑛2,𝑛3,𝑛4)	Re(𝑒𝐴)	Im(𝑒𝐴)	Re(𝑒𝐵)	Im(𝑒𝐵)
(8, 8, 8, 8)	3.943𝑒−4	2.459𝑒−4	6.255𝑒−4	2.832𝑒−4
(16, 8, 8, 8)	4.730𝑒−4	2.351𝑒−4	6.756𝑒−4	2.701𝑒−4
(8, 16, 8, 8)	1.400𝑒−4	1.472𝑒−4	3.007𝑒−4	1.688𝑒−4
(8, 8, 16, 8)	1.400𝑒−4	1.472𝑒−4	3.007𝑒−4	1.688𝑒−4
(8, 8, 8, 16)	4.730𝑒−4	2.351𝑒−4	6.756𝑒−4	2.701𝑒−4
Post-error	3.134𝑒−4	1.953𝑒−4	4.902𝑒−4	2.277𝑒−4
SEA-error	6.841𝑒−6	4.125𝑒−6	2.080𝑒−6	8.284𝑒−6
(16, 16, 16, 16)	4.534𝑒−5	2.849𝑒−5	7.934𝑒−5	2.973𝑒−5
(32, 16, 16, 16)	5.438𝑒−5	2.724𝑒−5	8.549𝑒−5	2.788𝑒−5
(16, 32, 16, 16)	1.648𝑒−5	1.729𝑒−5	3.849𝑒−5	1.859𝑒−5
(16, 16, 32, 16)	1.648𝑒−5	1.729𝑒−5	3.849𝑒−5	1.859𝑒−5
(16, 16, 16, 32)	5.438𝑒−5	2.724𝑒−5	8.549𝑒−5	2.788𝑒−5
Post-error	3.541𝑒−5	2.225𝑒−5	1.900𝑒−5	4.377𝑒−5
SEA-error	1.275𝑒−8	1.442𝑒−8	1.398𝑒−8	1.867𝑒−8