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Forced response curves (FRCs) of nonlinear systems can exhibit complex behaviors, including hardening/softening behavior and bifurcations. Although topology optimization holds great potential for tuning these nonlinear dynamic responses,…
We propose Alternating Phase-Field Fourier Neural Networks (APF-FNNs) as a unified and physics-based framework for topology optimization. The approach decouples the design problem by representing the state, adjoint, and topology fields with…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions $(f,\Lambda)$ in one variable. Topology of the Liouville fibration of the given integrable system near…
We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…
This article is concerned with the reconstruction of obstacle $\O$ immersed in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
In this work, we propose a new signal routing method for solving routing problems that occur in the design process of semiconductor package substrates. Our work uses a topological transformation of the layers of the package substrate in…
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…
Feature-mapping methods for topology optimization (FMTO) facilitate direct geometry extraction by leveraging high-level geometric descriptions of the designs. However, FMTO often relies solely on Boolean unions, which can restrict the…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…
The demand for high-performance heat sinks has significantly increased with advancements in computing power and the miniaturization of electronic devices. Among the promising solutions, nanofluids have attracted considerable attention due…
Efficient thermal management in high-power electronic devices requires cooling channel designs that provide high heat removal while satisfying strict spatial and manufacturing constraints. This study presents a two-stage hierarchical…
Topological photonics and acoustics have recently garnered wide research interests for their topological ability to manipulate the light and sound at surfaces. Conventionally, the supercell technique is the standard approach to calculating…