Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport

rbMIT © MIT Software

The rbMIT © MIT Software package implements in Matlab® all the general RB algorithms. The rbMIT © MIT Software package is intended to serve both (as Matlab® source) "Developers" — numerical analysts and computational tool-builders — who wish to further develop the methodology, and (as Matlab® "executables") "Users" — computational engineers and educators — who wish to rapidly apply the methodology to new applications.  ("End-Users"  of Worked Problems will also make use of the package, but in "blackbox" fashion.) Requirements are (i) some but not extensive knowledge of both FE methods and RB methods, (ii) Matlab® Version 6.5 or newer on some reasonably fast platform, (iii) the Matlab® symbolic, pde, and optimizaton toolkits, and (iv) agreement to rbMIT © MIT usage, distribution, and citation terms and conditions upon download.

Note that COMSOL Multiphysics® users can invoke the COMSOL platform — adaptive mesh generation, finite element discretization, and matrix assembly/solution capabilities — to generate the necessary rbMIT offline database. To invoke the COMSOL rather than the Matlab® PDE engine the user should set the flag femOPT.codes='COMSOL' at the beginning of each rbU file.

The rbMIT © MIT Software streamlines much of the RB code development process: for any new problem of interest, the rbMIT ©MIT Software permits quick and "automatic" (i) problem formulation and construction of the FE discretization (on which the RB approximation is built), (ii) application of RB Offline tools, for (iii) generation of RB Offline/Online datasets, and finally (iv) exercise of the RB Online RB Evaluator Visualizer; all necessary Offline and Online tools are supplied and integrated.

The rbMIT Software is a companion to the Book: for each Part, the Software implements and the Book describes the RB method for a different class of problems. However, at present, the Software is a somewhat impatient companion: the Software for Parts II and IV — Coercive Affine Linear Elliptic Equations and "Coercive" Affine Linear Parabolic Equations, respectively — is ready before the Book Parts II and IV. We thus make the Software for Parts II and IV, along with stand-alone documentation, available now.

The review paper Reduced Basis Approximation and A Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations — Application to Transport and Continuum Mechanics (a condensed form of the Book Part II) can serve as short-term surrogate for the Book Part II. A review paper on Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Parabolic PDEs; Application to Real-Time Bayesian Parameter Estimation can serve as a short-term surrogate for the Book, Part IV.

The rbMIT Software and associated documentation for Coercive Affine Linear Elliptic (Part II) and "Coercive" Affine Linear Parabolic (Part IV) equations are available at

rbMIT Software Download .


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