Project title: Efficient Solution Methods for Large-Scale Optimization Problems
Constrained by Time-Dependent Partial Differential Equations
Dr. Andrei Draganescu has received a $443,691, three-year research grant from the Department of Energy (DE–SC0005455), for the period 2014–2017. The award, which includes funds to support a Graduate Research Assistant for the duration of the grant, is a continuation of an earlier DOE award for the project titled "Multilevel Techniques for Large-scale Inverse Problems" (DE–SC0005455, $387,022, 2010–2014).
Optimization problems constrained by partial differential equations (PDEs) is a research area to which the scientific and engineering communities have devoted an increased level of effort over the last decade. This is due both to the tremendous advances in high-performance computing technologies and to its wide range of applicability, e.g., optimal design of manufacturing processes, history matching for petroleum reservoir simulations, data assimilation for weather prediction.
However, just growth in computing power is insufficient for tackling PDE-constrained optimization problems at the same extreme scales at which the PDEs themselves can be solved: although current computing capabilities allow, in principle, for the numerical solution of PDEs with 10–100 billion unknowns, solving PDE-constrained optimization problems of comparable size still requires significant algorithmic development. The objectives of the proposed project are to develop, analyze, and implement efficient methods for solving large-scale optimization problems constrained by time-dependent PDEs, with particular focus on the linear algebraic aspects of the solvers.
Constrained by Time-Dependent Partial Differential Equations
Dr. Andrei Draganescu has received a $443,691, three-year research grant from the Department of Energy (DE–SC0005455), for the period 2014–2017. The award, which includes funds to support a Graduate Research Assistant for the duration of the grant, is a continuation of an earlier DOE award for the project titled "Multilevel Techniques for Large-scale Inverse Problems" (DE–SC0005455, $387,022, 2010–2014).
Optimization problems constrained by partial differential equations (PDEs) is a research area to which the scientific and engineering communities have devoted an increased level of effort over the last decade. This is due both to the tremendous advances in high-performance computing technologies and to its wide range of applicability, e.g., optimal design of manufacturing processes, history matching for petroleum reservoir simulations, data assimilation for weather prediction.
However, just growth in computing power is insufficient for tackling PDE-constrained optimization problems at the same extreme scales at which the PDEs themselves can be solved: although current computing capabilities allow, in principle, for the numerical solution of PDEs with 10–100 billion unknowns, solving PDE-constrained optimization problems of comparable size still requires significant algorithmic development. The objectives of the proposed project are to develop, analyze, and implement efficient methods for solving large-scale optimization problems constrained by time-dependent PDEs, with particular focus on the linear algebraic aspects of the solvers.
