SolveLinearSystem Jacobi method does not converge when used with AddKnownsToLinearSystem

[a-y-khan]

See GForge bug #841.

[github-actions[bot]]

Stale issue message

[dcwhite]

@jessdtate Any comments on this one?

[jessdtate]

Just for simplicity, here is the info from gforge:

[jessdtate]

The SolveLinearSystem Jacobi; preconditioners method does not converge when it is used with inputs from AddKnownsToLinearSystem. It does not appear to matter if the preconditioner option is selected or not.Compare the Defibrillation tutorial network cube_simulation.srn (in nets/Optional/Defib-Tutorial), which contains AddKnownsToLinearSystem, with the test network nets/Modules/Math/FE-BuildRHS-Example-cube.srn. The presence of AddLinkedNodesToLinearSystem does affect the bug.

This not-converging problem is not because the Jacobi method has a bug. The cause is that the matrix in "cube_simulation.srn" does not satisfy the convergence condition required by the Jacobi method. Let's say the Jacobi method is solving a linear system Ax=b, let A=D+R where D is the diagonal of A, and R is the remainder part. The Jacobi method requires that the spectral radius of the matrix inv(D)*R (i.e., the absolute value of the largest eigen value) should be less than

1. In "cube_simulation.srn", the largest 2 eigen values of inv(D)*R is 0.9981 and 0.9954, so the Jacobi method is extremely slow to converge.

The Module "AddKnownsToLinearSystem" has been verified by comparing it with another program that performs the same functionality but was developed separately and used for several years. Both modules return the same results.

[jessdtate]

I've reproduced this in SR5 and SR4. But it seems less like a bug an more like a numerical limitation of the problem. We should look at it some more.