An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs
| Autor: | Sebastian Götschel, Michael L. Minion |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Equation of state
Mathematical optimization Optimization problem Speedup Computer science Computation 65K10 65M55 65M70 65Y05 PFASST MathematicsofComputing_NUMERICALANALYSIS Numerical & Computational Mathematics 010103 numerical & computational mathematics parallel-in-time methods 01 natural sciences 65Y05 FOS: Mathematics 0101 mathematics Mathematics - Optimization and Control 65M70 65K10 Numerical and Computational Mathematics math.OC 65M55 Applied Mathematics Constrained optimization Computation Theory and Mathematics State (functional analysis) Optimal control Parabolic partial differential equation Computational Mathematics Optimization and Control (math.OC) Adjoint equation PDE-constrained optimization |
| Zdroj: | SIAM Journal on Scientific Computing, vol 41, iss 6 Götschel, Sebastian; & Minion, Michael L. (2019). An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs. Lawrence Berkeley National Laboratory: Retrieved from: http://www.escholarship.org/uc/item/5zm4b7kd |
| ISSN: | 1095-7197 1064-8275 |
| DOI: | 10.1137/19m1239313 |
| Popis: | To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. We also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches. |
| Databáze: | OpenAIRE |
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