What is the best method to solve large linear system equation (Ax=b) (A:million~ by million~)

The maxtix A is sparse from finite element analysis.

I have used backslash to solve the equation but I want to reduce the calculation time.

I also tried to use GPU acceleration but there is a memory limitation with Titan xp with 12Gb memory.

Answer 1

[Christine Tobler]

You can try one of the Iterative Methods and Preconditioners.

[Youngsuk Jung]

As I know, Matlab choose appropriate method to solve linear equation when I use backslash(\).

Is there any chance to improve the performance by using Iterative solve myself?

[Bruno Luong]

Why? MATLAB has also a bunch of iterative solvers to chose from: cgs, bicg, gmres, etc...

[Christine Tobler]

MATLAB chooses an appropriate direct solver in backslash. Using iterative solvers requires more trial and error, and more knowledge of the original system (as preconditioners are often necessary). For a large, well-conditioned matrix, there can be a significant speed-up compared to backslash, if a suitable iterative solver is used.