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Theory
The TMG Correlation solver uses different optimization aglorithms to solve the objective function based on the governing equation; all described in this section.
References
The TMG Correlation optimization approach is based on the published scientific papers listed on the following page.

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User help
- Introduction to TMG Correlation
- TMG Correlation workflow
- TMG Correlation interface
  The TMG Correlation user interface is integrated in Simcenter 3D using NX Designcenter Open and contains unique features to conduct a thermal correlation analysis, in addition to standard tools and commands described in the Simcenter 3D Online help and the NX Designcenter Online help.
- Thermal correlation analysis preparation
  Before conducting a thermal correlation analysis, it is important to properly prepare your simulation model and the reference data.
- Understanding thermal correlation analysis
  The thermal correlation is a calibration process that helps you find the best thermal solution that minimizes the error between the computed and target temperatures at different locations and times.
- Managing the reference data
  In TMG Correlation, reference data refers to the temperature and time data that come from experimental tests or from prior and validated simulation models. They are named sensors and are used as targets for the optimization of the correlated solution.
- Understanding design variables
  A design variable is a simulation quantity of your model that the TMG Correlation solver varies within a specific range during the optimization to reduce the gap between the reference data and the simulation results.
- Setting up the optimization
  In optimization, the goal is to find values for the design variables that minimize the difference between the reference data and the correlated solution results.
- Monitoring the optimization
  Use the Solution Monitor and Solution Control Monitor to track the analysis during the solve. The monitors provide solver-specific information for the TMG thermal solver and the thermal correlation analysis.
- Analyzing the optimization results
  After you solve a thermal correlation analysis, you can analyze the results of the optimization process in the TMG Correlation dialog box.
- Updating the simulation model
  After you verified the optimization results, you must update the simulation model to reflect any changes that were made during the thermal correlation analysis so that you can continue your modeling in Simcenter 3D.
- Theory
  The TMG Correlation solver uses different optimization aglorithms to solve the objective function based on the governing equation; all described in this section.
  - Governing equation
    TMG Correlation optimizes the temperatures computed by the TMG thermal solver that solves for the heat conduction in a solid domain.
  - Objective function
    The TMG Correlation optimizer minimizes the objective function, F, that represents the error between the computed and target temperatures at different locations and times.
  - Adjoint-based optimization approach
    TMG Correlation uses gradient-based optimization algorithms, which rely on computing the gradient of the objective function. The gradient is the variation of the objective function with respect to the design variables. TMG Correlation uses the adjoint method to compute the gradient.
  - Optimization algorithms
    TMG Correlation computes the step length, α, when updating the design variable vector using the specified optimization algorithm method. All methods are local gradient-based optimization algorithms.
  - References
    The TMG Correlation optimization approach is based on the published scientific papers listed on the following page.
- Reference manuals
  This page contains links to thermal solver manuals that explain how the solver operates and how to use its various features.
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- License agreement
Installation guide
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References

The TMG Correlation optimization approach is based on the published scientific papers listed on the following page.

Michaleris, Panagiotis, Daniel A. Tortorelli and Creto A. Vidal. “Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity”. International Journal for Numerical Methods in Engineering 37, no 14 (1994) : 2471-2499.
Johnson, Steven G. The NLopt nonlinear-optimization package, http://github.com/stevengj/nlopt, 2007.
Svanberg, Krister. “A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations”. SIAM Journal on Optimization 12, no 2 (2002) : 555-573.
Kraft, Dieter. A Software Package for Sequential Quadratic Programming. Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt Köln : Forschungsbericht. . Wiss. Berichtswesen d. DFVLR, 1988.
Kraft, Dieter.“Algorithm 733 : TOMP–Fortran modules for optimal control calculations”. ACM Transactions on Mathematical Software (TOMS) 20, no 3 (1994) : 262-281.
Conn, Andrew R., Nicholas I. M. Gould and Philippe Toint. “A Globally Convergent Augmented Lagrangian Algo-rithm for Optimization with General Constraints and Simple Bounds”. SIAM Journal on Numerical Analysis 28, no 2 (1991) : 545-572.
Birgin, Ernesto G. et José M. Martínez. “Improving ultimate convergence of an augmented Lagrangian method”. Optimization Methods Software 23, no 2 (avril 2008) : 177-195.
Nocedal, Jorge. “Updating Quasi-Newton Matrices with Limited Storage”. Mathematics of Computation 35, no. 151 (1980): 773-82.
Liu, Dong C. et Jorge Nocedal. “On the limited memory BFGS method for large scale optimization”. Mathematical Programming 45 (1989) : 503-528.