1. 1 Taylor Series Expansion of the Green’s Function Green’s function between two points (x j, y j ) and (x i, y i ), which are the centroids of two interacting triangles, can be evaluated indirectly, first from (x j, y j ) to its nearest grid point (x j0, y j0 ), then from (x j0, y j0 ) to another grid point (x i0, y i0 ), and finally from (x i0, y i0 ) to (x i, y i ).

2. 2 Taylor Series Expansion of the Green’s Function the evaluation of the matrix-vector multiplication for the far- interaction contributions can then be read as

3. 3 Discussions the block-diagonal matrix [T s ] corresponds to a pre- multiplication, while the other block-diagonal matrix [T t ] corresponds to a post-multiplication the pre-multiplication corresponds to shifting the centroids of the basis triangles to their nearest grid points the multiplication of the block-Toeplitz matrix corresponds to computing all the interactions among the uniformly canonical grid points the final post-multiplication corresponds to translating the interactions at the grid points back to the centroids of the testing triangles the multiplication with the block-Toeplitz matrix can be then performed by FFT’s

4. 4 Verification of Numerical Results

5. 5

6. 6 Convergence of Iterative Solution

7. 7 Current Distributions

8. 8 Current Distribution for a Large-Scale Problem