We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.
An efficient preconditioner for evolutionary partial differential equations with $θ$-method in time discretization
An all-at-once preconditioner for evolutionary partial differential equations
Error estimation for the time to a threshold value in evolutionary partial differential equations
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