Related papers: Mixed variational formulations for structural topo…
This paper presents phononic band-structure calculation results obtained using a mixed variational formulation for 1-, and 2-dimensional unit cells. The formulation itself is presented in a form which is equally applicable to 3-dimensiomal…
In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a…
We consider optimal control of an elliptic two-point boundary value problem governed by functions of bounded variation (BV). The cost functional is composed of a tracking term for the state and the BV-seminorm of the control. We use the…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
This paper presents a novel variational formulation to simulate linear free-surface flow. The variational formulation is suitable for higher-order finite elements and higher-order and higher-continuity shape functions as employed in…
In this work, we investigate a nonconforming finite element approximation of phase-field parameterized topology optimization governed by the Stokes flow. The phase field, the velocity field and the pressure field are approximated by…
We develop a variational framework for addressing two-dimensional non-integrable quantum field theories through the exact structure of their integrable counterparts. Concentrating on the $\varphi^4$ Landau-Ginzburg model, we use the…
Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
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…
We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.…
A four-field mixed variational principle is proposed for large deformation analysis of Kirchhoff rods with a $C^0$ mixed FE approximations. The core idea behind the approach is to introduce a one-parameter family of points (the centerline)…
We present a new framework for solving general topology optimization (TO) problems that find an optimal material distribution within a design space to maximize the performance of a structure while satisfying design constraints. These…
We discuss a topology optimization problem for an elastoplastic medium. The distribution of material in a region is optimized with respect to a given target functional taking into account compliance. The incremental elastoplastic problem…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…