Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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If you can solve the linear system with a direct solver, then that's exactly what you should be doing. Multigrid is a method that can be used if you don't have the time or memory resources to use a direct solver (because direct solvers have a complexity that grows faster than $O(N)$ with the size of a linear system). If you use a direct solver as a sub-step ...

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Based on the image that you provided in your comment, I believe you formulate your problem as a system of PDEs for each branch in your network and make sure at each connecting node mass is conserved. Let's say you have $N$ branches, so you need to solve the system of advection-diffusion equations for each branch ($1 \leqslant i \leqslant N$): $$\frac{\... 1 I think you are using a downwind- instead of an upwind finite difference. This leads to your code imposing a boundary condition where it is not allowed. The solution to your convection equation is basically (ignoring the left BC for the moment)$$ C(x,t) = C_0(x - v t) $$where C_0 is your initial value. Thus, if v > 0, it is a rightward travelling ... 1 I think that the second boundary condition equation is incorrect. The first one should be right for both ends. Following your notation, the flux of mass in the domain should be:$$N = vC - D \frac{\partial C}{\partial x} everywhere including the boundary points. Keep in mind that the sign of the boundary condition value is positive if the direction of ...

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