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Project: Optimization with PDE constraints

Partial differential equations (PDEs) are used to model a multitude of phenomena in science and engineering. PDE-constrained optimization problems arise in e.g., environmental, and mechanical engineering, mathematical finance, and medicine.

Project information

Project manager at Linnaeus University
Christian Engström
Other project members
Eddie Wadbro, Karlstad University, Sweden
Juan-Carlos Araujo-Cabarcas, Umeå University, Sweden
Participating organizations
Linnaeus University, Karlstad University and Umeå University, Sweden
Linnaeus University
Mathematics (Department of Mathematics, Faculty of Technology)

More about the project

The goal of shape and topology optimization is to find a design that minimizes a given cost functional while satisfying PDE constraints. The space of admissible shapes is an infinite-dimensional space, which after discretization is reduced to finite dimension. The number of design variables in the discrete optimization problem is typically in the order of thousands or millions. This increases the chances of finding new designs with superior performance.

In the project, we analyze and develop:

  1. Efficient algorithms for topology and shape optimization.
  2. Existence and uniqueness of weak solutions for new applications.

The project is part of the research in the Scientific Computing and Partial Differential Equations research group.