The rbMIT © MIT Software* is a package for rapid and reliable prediction of engineering outputs associated with parametrized partial differential equations. The software is particularly well-suited to the many-query and real-time contexts.
At present, the software treats parametrized (scalar and vector) elliptic and parabolic linear coercive partial differential equations in planar and axisymmetric two-dimensional geometries. Parameters can be introduced to describe the domain geometry, the coefficients of the PDE, the sources, the boundary conditions, and the initial conditions. Applications include steady and unsteady heat transfer and convection-diffusion, and linear elasticity for isotropic and orthotropic media.
The rbMIT © MIT Software automates much of the reduced basis (RB) code development process: users can specify the problem in a simple high-level symbolic preprocessor. The software is intended to serve both (as Matlab® source) "Developers" — numerical analysts and computational tool-builders who wish to further develop the RB methodology; and (as Matlab® "executables") "Users" — computational engineers and educators who wish to rapidly apply the RB methodology to new applications. The software requires Matlab® Version 6.5 or newer and the Matlab® Symbolic, PDE, and Optimizaton Toolkits.
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. Once the offline database is created, the user can apply the rbMIT online codes: for any given parameter value, the online evaluator provides the desired output and rigorous output error bound (relative to the finite element model) very rapidly. Online visualization is also possible. 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 and associated documentation for elliptic and parabolic problems can be downloaded. A collection of model problems is also provided to illustrate various capabilities of the software and to allow "learning by example."
*MIT Technology Licensing Office, Case 12600.