arpit-babbar / renshu Goto Github PK

This thread will be used to keep track of performance of Julia Code, all changes made for it and their results.

The first commit about performance is Timer, option to skip plotting where a timer is added to solve functions and run files now have an option of skipping plotting. Currently, with fastest flux(HLL), the time taken is 0.023 seconds(23 millliseconds) for 100 points.

Ignore this.

Diagonalization of the matrix is done every time the numerical scheme is called. This was done with the idea that, in a non-linear system, since Jacobian is different from every point, diagonalization-dependent methods would require us to diagonalize every time. However, this must now be changed for efficiency purposes, because even in a non-linear system, we would make full use of the knowledge of the system to diagonalize efficiently.

https://github.com/Arpit-Babbar/arpit_practise/blob/a0e0efd3eb84ffb476334c085ab5017826b6462a/hyperbolic_systems/EqLinAdv.jl#L25

The code is currently relying on the explicit formula for a generalized flux, i.e., a formula for computing, for any diagonal(i.e., eigenvalue matrix) matrix L, QLQ^-1 where Q is the eigenvector matrix. This is the approach from the original paper. We need to be sure of the following

• Is this a better approach than what is suggested in hypsys notes? Are there better approaches?
• What is the most efficient way to take this approach while minimizing floating point operations?
• What is the best way to do with fewest lines? There's too much code duplication. The obvious idea is to have a sub-function. But, is it efficient for a sub-function to use variables that are not local to it. It's not okay for it use global variables, but is it okay for it to use variables that are local to the main function? This is easy to check with benchmarks.
• Order eigenvalues in increasing order.

Lastly,

• what is our stance on using the Julia Math symbols? They make code shorter, but does it really improve readability?

EDIT -

• There's a line longer than 80 characters there, it should be fixed.

https://github.com/Arpit-Babbar/arpit_practise/blob/ed1098694b22207f12dbd9fac793d07e0e7fe2f5/hyperbolic_systems/EqEuler.jl#L53

Currently, time step is computed as dt = dx/maximum_eigenvalue and the same function export dt and lam=dx/dt. This approach is for high efficiency, i.e., to avoid computing lam = dx/dt whenever numerical flux is computed. However, we'd let this minute performance dip for the moment.

https://github.com/Arpit-Babbar/arpit_practise/blob/ed1098694b22207f12dbd9fac793d07e0e7fe2f5/hyperbolic_systems/EqEuler.jl#L53

https://github.com/Arpit-Babbar/arpit_practise/blob/1266da8fa23aa58a020ce1ca6c0f772cf2a608e0/fd2d_var_coefficients/fd2d_var.cc#L10

To merge

1. fv2d, fv2d_dirichlet and fv2d_var_coeff
2. linear_convection_1d, back_lw and linear_convection_1d_limiter_functions
   To potentially remove
3. fd2d, fd2d_var_coeff