WAVE-FORM KRYLOV SUBSPACE METHODS ON A MASSIVELY-PARALLEL COMPUTER

Recently, the waveform generalized minimal residual method (WGMRES) wa s proposed for solving differential-algebraic equations problems. Base d on this, several waveform Krylov subspace methods are developed for comparison. Particularly, we propose using an adjoint operator for the waveform bi-conjugate gradient method and the waveform quasi-minimal residual method. The difficulties of developing the adjoint operator w ill be addressed. Furthermore, these methods are applied to solve a la rge sparse linear system of ordinary differential equations arising fr om a parabolic partial differential equation on a DECmpp 12000/Sx para llel computer for comparison. Numerical results show that the WGMRES m ethod and the waveform bi-conjugate gradient stabilized method can ach ieve better performance than the conventional waveform relaxation meth ods.