A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains
Table 2
Number of iterations and computational time required by the FC solver and the finite difference solver to compute to a fixed accuracy for the unit square example (fixed boundaries). (The first 10 eigenvalues are calculated to the tolerance of , but we only show the error in the first eigenvalue for conciseness.) For each given accuracy, the FC(Gram) algorithm outperforms the finite difference algorithm by a large margin. All computations were performed on a 2.67 GHz Intel Xeon processor. (a) Results using centered finite difference; (b) results using FC(Gram) with 5th-order basis.
