Related papers: Fluidic Shaping over arbitrary domains: theory and…
We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…
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…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
Accurate triangulation of the domain plays a pivotal role in computing the numerical approximation of the differential operators. A good triangulation is the one which aids in reducing discretization errors. In a standard collocation…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…
An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
In this article, we develop a least--squares/fictitious domain method for direct simulation of fluid particle motion with Navier slip boundary condition at the fluid--particle interface. Let $\Omega$ and $B$ be two bounded domains of…
A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
Fluidic devices are crucial components in many industrial applications involving fluid mechanics. Computational design of a high-performance fluidic system faces multifaceted challenges regarding its geometric representation and physical…
We propose a novel cut finite element method for the numerical solution of the Biot system of poroelasticity. The Biot system couples elastic deformation of a porous solid with viscous fluid flow and commonly arises on domains with complex…
In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the…
A new adaptive shaping method that can generate arbitrary optical waveforms with folded-type or fan-type birefringent variable shapers is proposed in this paper. Automatic arbitrary laser temporal shaping of picosecond and femtosecond…
A novel method for complex fluid-structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed-grid)…
Mechanochemical processes on surfaces such as the cellular cortex or epithelial sheets, play a key role in determining patterns and shape changes of biological systems. To understand the complex interplay of hydrodynamics and material flows…
This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
Characteristic modes are formulated using the scattering dyadic, which maps incident plane waves to scattered far fields generated by an object of arbitrary material composition. Numerical construction of the scattering dyadic using…