The study presents a fast and efficient approach to calculating electromagnetic fields based on FFT-GFIEM and GMRES with restarts for solving linear equations with grids ranging from \(128 \times 128\) to \(8192 \times 8192\) . For \(k \ge 35\) , the algorithm achieves tolerance without restarts for smaller matrices; however, memory overflow occurs for larger sizes. The use of restarts enables reaching tolerance on larger matrices while reducing memory usage by approximately tenfold, although this increases the number of operations correspondingly. Future work may enhance accuracy through the application of non-uniform grids, although this could limit the applicability of Toeplitz matrices and consequently reduce computational speed. The results may be beneficial for the design of photonic components.