Jacobi
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.
General
Settings When Not Used with Coarse Solver
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.
With the Molecular Flow Module plus the Particle Tracing Module, see Molecular Flow Through an RF Coupler: Application Library path Molecular_Flow_Module/Benchmarks/rf_coupler.
Settings When Used With a Coarse Solver
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:
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Relative tolerance to specify the termination tolerance. The default is 0.1.
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Maximum number of iterations that the solver is allowed to take. When this number of iterations has been performed without reaching the tolerance specified in the Relative tolerance field, the solver is automatically stopped with an error message.
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.