相关论文: Comparison of Shape Derivatives using CutFEM for I…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
We revisit the problem of identifying an unknown portion of a boundary subject to a Robin condition based on a pair of Cauchy data on the accessible part of the boundary. It is known that a single measurement may correspond to infinitely…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
The Stokes problem with non-homogeneous Dirichlet boundary condition is solved numerically using conforming discretizations and an approximation of the boundary datum in the corresponding trace space. Optimal discretization error estimates…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite…
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture…
In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality…
We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for…
This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
In this work, we analyze a penalized variant of the {\phi}-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The {\phi}-FEM is a recently introduced unfitted finite element method based on a level-set description of…
For an educational purpose we develop the Python package AutoFreeFem which generates all ingredients for shape optimization with non-linear multi-physics in FreeFEM++ and also outputs the expressions for use in LaTex. As an input, the…