I’m solving a diffusion problem of several connected domains. I use a Crank-Nicolson scheme on each domain, and at every time step I connect the domains by some matching conditions at the boundary. To do the Crank-Nicolson I have to do u = A\b, at every time step for each domain, where u is the solu…

Welcome to Julia Discourse! You will find many experts here on numerical linear algebra and solutions of partial differential equations. I am not one of them, but I do have a couple of suggestions. I think you might get more responses if you showed in more explicit detail what you’ve attempted so…

[image] lhcgeneva: with the difference that u and b change at every time step. I’d then do u_1 = A_1\b_1 u_2 = A_2\b_2 u_3 = A_3\b_3 If the matrices stay the same, while only u and b change on each timestep, then you should definitely precompute the matrix factorizations. e.g. precompute F…

Also, is there a specific reason you are using hand-written Crank-Nicolson? You likely will get better results with OrdinaryDiffEq.jl which would let you use much fancier solvers easily.

Great, thanks everyone! The factorisation / lu decomposition made a 20% difference already. @Oscar_Smith : I’m interested in this! So here’s the problem stated a bit more formally. Could you give me a few keywords/hints on how to use OrdinaryDiffEq.jl effectively to solve this quicker than using bac…

Best performance for initialising a variable number of matrices/vectors within a Crank-Nicolson scheme

General Usage Performance

Topic		Replies	Views
Parallelizing multiple Crank–Nicolson solvers Performance linearalgebra	21	1587	March 13, 2021
Improving Performance of For-Loop and Matrix Multiplication for Time Integration Solver Performance loops , matrices	8	1198	June 1, 2020
Solving a linear system without modifying and allocating arrays Performance	3	176	March 25, 2025
Optimising iterative solution of small system Performance linearalgebra	12	555	April 16, 2024
Speeding up solving `Ax=b` repeated when `A` is partially updated Performance linearalgebra	4	942	December 29, 2022

Best performance for initialising a variable number of matrices/vectors within a Crank-Nicolson scheme

Related topics