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TW 326
J. Hendrickx, R. Vandebril, M. Van Barel
A fast method for solving the two-dimensional Helmholtz equation with Robbins boundary conditions
Abstract
We present a fast direct method for solving the two-dimensional Helmholtz equation: on a rectangular grid [0,a1]x[0,a2] with Robbins boundary conditions. Because we can solve the Helmholtz equation, with Neumann boundary conditions in a fast way using the discrete cosine transform, we can split the problem above into two smaller problems. One of these problems can be solved using the same techniques as in the Neumann-boundary case. The second, and the hardest problem of the two, can be solved using low displacement rank techniques. When dividing [0,a1] into n1 and [0,a2] into n2 equal parts, the total complexity of the overall algorithm is 10 n1n2 log(n2) + O(n1^2 + n1n2), which gives us a fast algorithm.
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