MATRIX-FREE W-METHODS USING A MULTIPLE ARNOLDI ITERATION

The standard Arnoldi method approximates the solution of one single li near system through projection onto a Krylov space constructed from th e right-hand side vector. The different stage equations of a W-method use the same matrix but different right-hand sides, which are, in gene ral, not part of the original Krylov space. For the case of two right- hand sides we discuss two well-known deterministic strategies that ext end the Arnoldi process from the first stage and present a new one tha t performs Krylov steps adaptively to minimize the residual of the nex t approximation. An implementation of these methods is tested on three different parabolic problems and compared with the code VODPK.