Invited Session Wed.2.H 1058

Wednesday, 13:15 - 14:45 h, Room: H 1058

Cluster 10: Implementations & software [...]

Software for PDE-constrained optimization


Chair: Denis Ridzal



Wednesday, 13:15 - 13:40 h, Room: H 1058, Talk 1

Joseph Young
Software abstractions for matrix-free PDE optimization with cone constraints

Coauthor: Denis Ridzal


In this presentation, we describe algorithms and software
abstractions for a matrix-free code for PDE constrained
optimization problems that contain both equality as well
as cone constraints. The key to our discussion lies in
the development of simple algebraic abstractions that allow
us to build an efficient code and how these abstractions
change between the different kinds of constraints. In
addition to the theoretical and practical utility of this
approach, we integrate these ideas into a new matrix-free
code called ROL and present numerical examples.



Wednesday, 13:45 - 14:10 h, Room: H 1058, Talk 2

Andreas Potschka
MUSCOP: A multiple shooting code for time-periodic parabolic PDE constrained optimization

Coauthor: Hans-Georg Bock


Time-periodic parabolic PDE constraints arise in important applications in chemical engineering, e.g., in periodic adsorption processes. We present the software package MUSCOP which was designed to solve such optimization problems. The GNU Octave/C++ code is based on a hybrid programming principle to allow for rapid development without sacrificing computational speed. Algorithmically, MUSCOP is based on the Method of Lines, Direct Multiple Shooting, inexact Sequential Quadratic Programming, and indefinite two-grid Newton-Picard preconditioning. For the generation of first and second order derivatives, MUSCOP relies heavily on Internal Numerical Differentiation and Algorithmical Differentiation within the adaptive C++ integrator suite SolvIND and the package ADOL-C. We explain the parallelization and mathematical exploitation of structures arising from the Direct Multiple Shooting and the two-grid approach. Grid-independent convergence can be observed in the numerical experiments and even be proved for a typical model problem. We conclude the talk with numerical results for problems ranging from academic models to a real world SMB process.



Wednesday, 14:15 - 14:40 h, Room: H 1058, Talk 3

Drosos Kourounis
Gradient-based optimization using adjoint methods for optimization of compositional flow in porous media


Adjoint-based gradients form an important ingredient of fast
optimization algorithms for computer-assisted history matching and
life-cycle production optimization. Large-scale applications of
adjoint-based reservoir optimization reported so far concern
relatively simple physics, in particular two-phase (oil-water) or
three-phase (oil-gas-water) applications. In contrast, compositional
simulation has the added complexity of frequent flash calculations and
high compressibilities which potentially complicate both the adjoint
computation and gradient-based optimization, especially in the
presence of complex constraints. These aspects are investigated using
a new adjoint implementation in a research reservoir simulator
designed on top of an automatic differentiation framework coupled to a
standard large-scale nonlinear optimization package. Optimization of
strongly compressible flow with constraints on well
rates or pressures leads to slow convergence and potentially poor
performance. We present a pragmatic but effective strategy to overcome this issue.


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