The site comprises a number of illustrative Worked Problems — defined by governing equations, parameter domain, and outputs of interest — in solid mechanics, heat transfer, acoustics, and fluid dynamics. Each problem is characterized by a vector of *P *input parameters and an associated input domain ; and a scalar output representing the engineering quantity of interest.

For each Worked Problem, the End-User can rapidly and reliable predict the parametric dependence of the output: Given an input parameter value, the RB Online Evaluator returns — typically in milliseconds — both (*a*) an accurate RB prediction for the output, and (*b*) a certificate of fidelity that rigorously bounds the error in the RB prediction relative to a highly accurate finite element solution. We thus achieve educationally (and design) relevant "interactive timescales" with little or no compromise in accuracy *or *certainty.

The software also includes a RB Visualizer which, given an input parameter value, (*a*) renders the relevant field variable, and (*b*) provides an associated rigorous bound for the error in the RB field relative to the finite
element field. This feature is somewhat slower and more memory-intensive, but also more "physical" and colorful.

The End-User can access the RB Online Evaluator and RB Visualizer for a particular Worked Problem in two fashions: with limited functionality and some degradation in performance — but very simply — through our Matlab® webserver; or with full functionality and optimal performance — but with a bit more effort — downloaded to the End-User's own computer.

Note for the download option, the user must first download the necessary rbMIT Software and documentation. Then, for each Worked Problem available (see below or sidebar), we provide for download the necessary user input file. The End-User must execute several commands indicated in Sections I., II., and
III. of the rbMIT documentation to generate the RB Online Evaluator and RB Visualizer functions (for any particular Worked Problem); the End-User is *not* required to understand the software, make any choices, or provide any
arguments — except ultimately the desired parameter values for output evaluation or field visualization.

The* Worked Problems *available are:

*Solid Mechanics*

CenterCrack

*Heat Transfer*

Heterogeneous Thermal Block

Thermal Contraction Resistance

Thermal Fin

The "Graetz" Problem

Nonhomogeneous Semi-Infinite Body

A Transient Heat Treatment Problem

The Transient Convection-Diffusion Problem Around a Cylinder

Transient Forced Convection: Heating Duct

*Acoustics*

*Fluid Mechanics*

The "addedmass" Problem in Hydrodynamics

Venturi: Potential Flow

Circular Bend: Potential Flow

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