Diagonal preconditioners for the EFIE using a wavelet basis

The electric field integral equation (EFIE) has found widespread use and in practice has been accepted as a stable method, However, mathematically, the solution of the EFIE is an ''ill-posed'' problem, In practical terms, as one uses more and more expansion and testing functions per wavelength, the condition number of the resulting moment-method matrix increases (without bound), This means that for high-sampling densities, iterative methods such as conjugate gradients converge more slowly, However, there is a way to change all this, The EFIE is considered using a wavelet basis for expansion and for testing functions, Then, the resulting matrix is multiplied on both sides by a diagonal matrix, This results in a well-conditioned matrix which behaves much like the matrix for the magnetic field integral equation (MFIE), Consequences for the stability and convergence rate of iterative methods are described.