Efficiensy study of solution methods for discrete optimization problems, constrained by partial differential equations
Dnr:  SNIC 2016/7121 
Type:  SNAC Small 
Principal Investigator:  Maya Neytscheva 
Affiliation:  Uppsala universitet 
Start Date:  20161201 
End Date:  20181201 
Primary Classification:  10105: Beräkningsmatematik 
Webpage:  
Allocation
Abstract
Optimal design, optimal control and parameter estimation of systems governed by partial differential equations (PDE) give rise to a class of problems, referred to as PDEconstrained optimization problems (OPTPDE).
These problems arise in many important applications. As the name suggests, in the OPTPDE framework optimization methods are coupled with methods to numerically solve PDEs. The task is to steer the solution of some process in order to fulfill various requirements
imposed on it. A classical example is the construction of a machine to meet some desired performance specifications. These problems can also involve finding some unknown parameter function in the equation, which is then estimated based on a control function in the form of measurements, in the interior or on the boundary of the domain of definition of the PDE.
In such problems one must solve discretized PDEs many times and, unless properly handled, this can demand an unfeasible amount of computational labor, computer time and memory, even on the presently available high performance computers. Because of the large number of
degrees of freedom, much larger than when we only solve discrete PDE problems, iterative methods are the methods of choice and, therefore, constructing efficient preconditioners for this class of problems remains a hot topic of research. Highly parallelizable and numerically efficient preconditioning techniques and their
performance on HPC computer platforms is the central topic of this project.
