Successive Under-Relaxation
E621091
Successive Under-Relaxation is a numerical technique for iteratively solving linear systems that deliberately uses a relaxation factor less than one to slow updates and improve stability or convergence in certain problems.
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf | iterative numerical method ⓘ |
| alsoKnownAs | SUR NERFINISHED ⓘ |
| appliesTo |
discretized partial differential equations
ⓘ
linear algebraic systems ⓘ |
| belongsTo |
iterative methods for sparse systems
ⓘ
numerical linear algebra ⓘ |
| canBeCombinedWith |
Gauss–Seidel iteration
NERFINISHED
ⓘ
Jacobi iteration ⓘ |
| contrastsWith | Successive Over-Relaxation which uses omega > 1 ⓘ |
| dependsOn | choice of relaxation factor for performance ⓘ |
| goal | to obtain stable convergence for difficult systems ⓘ |
| hasConstraintOnParameter | 0 < omega < 1 ⓘ |
| hasEffect |
increases robustness of convergence
ⓘ
reduces step size of each iteration ⓘ |
| hasMathematicalForm | x^{k+1} = x^{k} + omega (x^{k+1}_{*} - x^{k}) ⓘ |
| hasParameter | omega ⓘ |
| hasProperty |
can prevent divergence in unstable schemes
ⓘ
can slow nominal convergence rate ⓘ damps oscillations in iterative updates ⓘ relaxation factor less than one ⓘ |
| hasPurpose |
to improve convergence behavior in some problems
ⓘ
to improve stability of iterative schemes ⓘ to iteratively solve linear systems ⓘ |
| isBasedOn | relaxation techniques ⓘ |
| isRelatedTo |
Gauss–Seidel method
NERFINISHED
ⓘ
Jacobi method NERFINISHED ⓘ Successive Over-Relaxation NERFINISHED ⓘ |
| isUsedIn |
computational fluid dynamics
ⓘ
engineering simulations ⓘ finite difference methods ⓘ finite element methods ⓘ finite volume methods ⓘ iterative solution of Poisson equations ⓘ steady-state solvers ⓘ |
| modifies | update step of an iterative method ⓘ |
| optimizationCriterion | trade-off between stability and speed of convergence ⓘ |
| typicalUseCase |
highly nonlinear or stiff problems
ⓘ
strongly coupled equations ⓘ |
| usesConcept | relaxation factor ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.