Research Article

A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains

Table 1

Computational time required for evaluation of the differential operator for four test cases, with breakdown of computing time per calculation, and the number of calculations needed for the eigenvalue solver to converge to the required tolerance. All computations were performed on a 2.67 GHz Intel Xeon processor. (a) Square with fixed edges; (b) square with one free edge; (c) disk with fixed boundary; (d) disk with free boundary.
(a)

Time per operation (s) Number of operations Total time in (s)

1525 0.001691 728 1.2313
6100 0.006096 2179 13.2835
24400 0.020961 6003 125.8296
97600 0.103420 22861 2364.2878

(b)

Time per operation (s) Number of operations Total time in (s)

1525 0.001891 923 1.7452
6100 0.005459 2702 14.7507
24400 0.019813 8328 165.0070
97600 0.094591 23440 2217.2179

(c)

Time per operation (s) Number of operations Total time in (s)

3950 0.006348 1065 6.7605
15800 0.017500 2037 35.6459
63200 0.072966 4981 363.4445
252800 0.257892 12338 3181.8739

(d)

Time per operation (s) Number of operations Total time in (s)

3950 0.006638 1584 10.5144
15800 0.012105 3336 40.3828
63200 0.061148 7027 429.6900
252800 0.222666 14820 3299.9156