PDE Seminar: "Domain decomposition integrators for nonlinear parabolic equations", Eskil Hansen (Lund)
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We will analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are well suited for integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a nonlinear parabolic system can then be interpreted as an operator splitting scheme applied to an abstract evolution equation governed by a maximal dissipative vector field. By utilizing this abstract setting, we derive an temporal error analysis for the most common choices of domain decmposition based integrators.