Related papers: A fully variational numerical method for structura…
Topology optimization (TO) is a well-established methodology for structural design under user-defined constraints, e.g. minimum volume and maximum stiffness. However, such methods have traditionally been applied to static, deterministic…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
We augment a thermodynamically consistent diffuse interface model for the description of line tension phenomena by multiplicative stochastic noise to capture the effects of thermal fluctuations and establish the existence of pathwise unique…
Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…
In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space…
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional…
Particle flow processing is widely employed across various industrial applications and technologies. Due to the complex interactions between particles and fluids, designing effective devices for particle flow processing is challenging. In…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is…
In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and…
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies…
In this work we propose a method to perform optimization on manifolds. We assume to have an objective function $f$ defined on a manifold and think of it as the potential energy of a mechanical system. By adding a momentum-dependent kinetic…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…