I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which start with an initial guess of the entire 2D grid u(x,t) and refine it iteratively. Although I came across multiple libraries which can solve 1D burgers, all of them generate the solution from time = 0 to the maximum_time. Whereas, I am looking for a solver which refines the solution for the whole space-time (2D in 1D burgers case) at once.
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$\begingroup$ it sounds like you want a space-time finite element method, however even these methods typically have relatively short extents in time $\endgroup$– helloworld922Commented Apr 23 at 4:20
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$\begingroup$ Hi, I have some Matlab code (as @helloworld922 mentioned, it is a space-time FEM) which solves Burger's equation for 1+1D in fairly general fashion (for example, the interval can be time-dependent). This functionality is also implemented in MFEM (mfem.org) by my PhD supervisor's (Sander Rhebergen) research group (hence partially by me). We also have implemented all-at-once ST-HDG methods which can solve temporal PDEs (memory permitting) over the whole time span simultaneously. $\endgroup$– Abdullah Ali SivasCommented Apr 23 at 5:26
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2$\begingroup$ It's hard to think of a good reason for rejecting the solvers you have found. Perhaps if you can explain why you want an iterative solver, we might be able to help you better. Otherwise there are some rather trivial ways to answer your question, but they probably aren't what you really want. $\endgroup$– David KetchesonCommented Apr 23 at 5:53
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2$\begingroup$ Why would you not want to solve the equation with a time stepping approach? $\endgroup$– Wolfgang BangerthCommented Apr 23 at 15:11
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1$\begingroup$ if you just need the solution at various times take a snapshot of the solution after taking a timestep, then stitch them together into a "2D" input space-time input for your network $\endgroup$– helloworld922Commented Apr 24 at 0:36
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