Repairing near-singularity for dense EMC problems by adaptive basis techniques

A standard boundary element method (BEM) discretisation for the electromagnetic compatibility (EMC) problem is analysed, revealing the near-singularity of the dense linear system for the lower frequency range. Next, a new basis transformation is presented, that separates the dominating capacitive eeects from the small, but important inductive eeects. On this basis a sparse approximate inverse is constructed, that is used not only as a preconditioner, but also as a smoother for a multi-level preconditioner. The number of matrix-vector multiplications for the iterative solver is further reduced by reusing information: Ritz vectors, obtained from previous right-hand side solves, are injected into the search space of GMRESR, thereby skipping the stagnation phase. Reuse of information from the previous frequency computations has also been attempted, but this is less eeective. Test results for the diierent methods are presented and compared.