Dakota Reference Manual: richardson_extrap

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richardson_extrap

Estimate order of convergence of a response as model fidelity increases

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required (Choose One) | Verification Mode (Group 1) | estimate_order | Compute the best estimate of the convergence order from three points
converge_order | Refine until the estimated covergence order converges
converge_qoi | Refine until the response converges
| Optional | refinement_rate | Rate at which the state variables are refined
| Optional | convergence_tolerance | Stopping criterion based on objective function or statistics convergence
| Optional | max_iterations | Number of iterations allowed for optimizers and adaptive UQ methods
| Optional | model_pointer | Identifier for model block to be used by a method

## Description

Solution verification procedures estimate the order of convergence of the simulation response data during the course of a refinement study. This branch of methods is new and currently only contains one algorithm: Richardson extrapolation.

Refinement of the model

The model fidelity must be parameterized by one or more continuous state variable(s).

The refinement path is determined from the `initial_state` of the `continuous_state` variables specification in combination with the `refinement_rate`, where each of the state variables is treated as an independent refinement factor and each of the initial state values is repeatedly divided by the refinement rate value to define new discretization states.

Results

Three algorithm options are currently provided:

1. `estimate_order`
2. `converge_order`
3. `converge_qoi`

Stopping Criteria

The method employs the `max_iterations` and `convergence_tolerance` method independent controls as stopping criteria.

## Theory

In each of these cases, convergence order for a response quantity of interest (QoI) is estimated from

where is the uniform refinement rate specified by `refinement_rate`.