The Jacobi node (
) is an attribute that handles settings for the Jacobi (or diagonal scaling) method. Right-click the
Iterative,
Krylov Preconditioner,
Presmoother,
Postsmoother, or
Coarse Solver attribute nodes to add a
Jacobi feature.
The Jacobi method provides a simple and memory-efficient solver/preconditioner/smoother based on classical iteration methods for solving a linear system of the form A x = b. Given a relaxation factor
ω (usually between
0 and
2), a sweep of the Jacobi (diagonal scaling) method transforms an initial guess
x0 to an improved approximation
x1 = x0 + M−1(b − Ax0), where
M = D/ω, and
D is the diagonal part of
A.
Enter the Number of iterations to perform when this node is used as a preconditioner or smoother. This setting is not considered when the attribute is used as a linear system solver (with the
Use preconditioner option in the
Solver list of the
Iterative attribute node). The solver then iterates until the relative tolerance specified by the corresponding operation node is fulfilled rather than performing a fixed number of iterations.
If this node is used with a Coarse Solver, select a
Termination technique to determine how to terminate the solver. Select
Fixed number of iterations to perform a fixed number of iterations each time the
Coarse Solver is used, or
Use tolerance to terminate the
Coarse Solver when a tolerance is fulfilled.
If Fixed number of iterations is selected, enter a value for the
Number of iterations to perform. The default is 10.
If Use tolerance is selected, enter a value for each of the following:
Also enter a Relaxation factor to specify a scalar relaxation factor
ω. The allowed values of this factor are between 0 and 2. The default is 1. See
About the Relaxation Factor for more information.