Efficient solution of block Toeplitz systems with multiple right-hand sides arising from a periodic boundary element formulation

Block Toeplitz matrices are a special class of that exhibit reduced memory requirements and complexity matrix-vector multiplications. We herein present an efficient computational approach to solve sequence block systems arising from system with multiple right-hand sides. Two different numerical schemes implemented for the solution based on global variants generalized minimal residual (GMRES) method. The performance is assessed in terms wall clock time iterative process, number multiplications matrix peak usage. To demonstrate method, two examples presented. In first case study, aeroacoustic prediction airfoil turbulent flow examined, which requires solutions pressure field beneath boundary layer. fluctuating surface synthesized uncorrelated plane waves, whereby each realization input acoustic solver element method (BEM). total response then obtained ensemble average realizations considered. yield converged leads systems. second study examines nonlinear eigenvalue analysis sonic crystal barrier composed locally resonant C-shaped sound-hard scatterers. periodicity sound whereas problem sequences linear combined technique using proposed GMRES shown computationally noise analysis.