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I thought the state-of-the-art method to solve PDE on meshes is to solve system of linear equations instead of the iterative update method, right? Then why are people interested in a language specific for the iterative method?


@pavelkang, because PDE is not a static state. If we are solving an ODE like LAPLACE equation, which correspond to the final state of heat equation, then solving a linear system is enough. For PDE like heat equation, it describes how heat spread out in a sequence of time steps. So it's intrinsically an iterative process over those time steps.

Even for solving linear systems, iterative methods are sometime used because we can stop early when the solution is already good enough. Besides, iterative methods are easy to be parallelized.