Related papers: A novel shape optimization approach for source ide…
We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the…
In this paper we consider a shape optimization problem for the minimization of the erosion, that is caused by the impact of inert particles onto the walls of a bended pipe. Using the continuous adjoint approach, we formally compute the…
In this paper, we introduce the Method of Ellipcenters (ME) for unconstrained minimization. At the cost of two gradients per iteration and a line search, we compute the next iterate by setting it as the center of an elliptical…
In this thesis we develop a functional analytic framework for shape optimization with elliptic partial differential equation (PDE) constraints in classical function spaces (H\"older spaces). This approach is motivated by shape optimization…
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and…
It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. The goal is to recover the…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of the control function. The state problem formulation is…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…