An Important Application of the Implicit HDG Time-Domain Method Based on Block GMRES for Multiple Right-Hand Sides

To solve the linear systems with multiple right-hand sides (RHS) arising from the implicit hybridizable discontinuous Galerkin time-domain method for electromagnetic simulations, we propose a block version of the generalized minimal residual method with deflated restarting technique. To accelerate convergence, two improvements are introduced. First, a better strategy is designed to select initial values for restarting a new round of iterations. Second, a multifrontal block incomplete Cholesky factorization is employed as the preconditioner. Numerical results demonstrate its efficiency in computing multiple RHS problems.