Bloch wave – MoM method the wave numbers in any of the 3 periodic coordinate directions. This can happen for example when the free space wavelength exactly equals the lattice spacing. This is a statistically rare occurrence in computational practice and corresponds to a propagation anomaly similar to a Wood's reflection anomaly for gratings. To compute bands of the crystal (i.e. "k"-"k" diagrams), successive values of frequency ("k") are tried - in conjunction with pre-selected values of propagation constant ("k") and propagation direction (θ & φ) - until a combination is found which drives the determinant of the matrix to zero. Equation (4.2) has been
Successive over-relaxation methods were designed for computation by human calculators, and they required some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young, Jr. Given a square system of "n" linear equations with unknown x: where: Then "A" can be decomposed into a diagonal component "D", and strictly lower and upper triangular components "L" and "U": where The system of linear equations may be rewritten as: for a constant "ω" > 1, called the "relaxation factor". The method of successive over-relaxation is an iterative