Model reduction of parabolic PDEs using multivariate splines

Sequential linear quadratic control of bilinear parabolic PDEs based on POD model reduction

We present a framework to solve a finite-time optimal control problem for parabolic partial differential equations (PDEs) with diffusivity-interior actuators, which is motivated by the control of the current density profile in tokamak plasmas. The proposed approach is based on reduced order modeling (ROM) and successive optimal control computation. First we either simulate the parabolic PDE sys...

Completion of overdetermined parabolic PDEs

In this paper we apply methods of commutative algebra to analysis of systems of PDEs. More precisely, we show that systems which are parabolic in a generalized sense are equivalent to certain completed systems which are parabolic in the standard sense. We also propose a constructive method to get this completion, and Gröbner basis methods, via symbol modules of the systems, play a central role ...

Numerical Optimal Control of Parabolic Pdes Using Dasopt

This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by time-dependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differential-algebraic equations (DAEs) with a package for large-scale optimization based on sequential quadratic programming (SQP). DASOPT is intended fo...

Approximation of parabolic PDEs on spheres using spherical basis functions

In this paper we investigate the approximation of a class of parabolic partial differential equations on the unit spheres S n ⊂ R n+1 using spherical basis functions. Error estimates in the Sobolev norm are derived.

Multivariate Adaptive Regression Splines