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T R O T T ' S C O R N E R
Michael Trott

Matrix Construction

We have to determine coefficients . To find them, we will have to use more equations than variables. (If we take the same number of equations as unknown coefficients, we would get a unique solution that makes the specified Fourier coefficients vanish but which could oscillate dramatically. See the following explicit numerical results.) Here, we will use Fourier modes along the circular arcs and modes along the longer Dirichlet parts of the center disk.

As mentioned earlier, we will use the cos-modes along the arcs joining the center disk with the left and right arm and the sin-modes along the Dirichlet part of the center disk. We could, of course, also use some of the sin modes along the joining arcs.

The function makeLHSAndRHS[prec, {d, e}] will construct the coefficient matrix and the right-hand side of the system of linear equations for the with equations.



     
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