Name
Abstract | ||
|---|---|---|
We present a nested multigrid method to optimize time-periodic, parabolic, partial differential equations (PDE). We consider a quadratic tracking objective with a linear parabolic PDE constraint. The first order optimality conditions, given by a coupled system of boundary value problems can be rewritten as an Fredholm integral equation of the second kind, which is solved by a multigrid of the second kind. The evaluation of the integral operator consists of solving sequentially a boundary value problem for respectively the state and the adjoints. Both problems are solved efficiently by a time-periodic space-time multigrid method. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00791-011-0158-4 | Computat. and Visualiz. in Science |
Keywords | Field | DocType |
time-periodic space-time multigrid method,quadratic tracking objective,parabolic optimal control problem,nested multigrid method,linear parabolic pde constraint,order optimality condition,fredholm integral equation,partial differential equation,integral operator,boundary value problem | Parabolic partial differential equation,Boundary value problem,Mathematical optimization,Mathematical analysis,Fredholm integral equation,Integral equation,Elliptic partial differential equation,Partial differential equation,Multigrid method,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
14 | 1 | 1433-0369 |
Citations | PageRank | References |
7 | 0.62 | 10 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dirk Abbeloos | 1 | 7 | 0.62 |
| Moritz Diehl | 2 | 1343 | 134.37 |
| M. Hinze | 3 | 185 | 20.26 |
| Stefan Vandewalle | 4 | 501 | 62.63 |