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We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown…
Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the…
An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the…
Phoretic particles exploit local self-generated physico-chemical gradients to achieve self-propulsion at the micron scale. The collective dynamics of a large number of such particles is currently the focus of intense research efforts, both…
The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity $\epsilon$ of one of the two solution…
In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As known, the solution variables (the pressure and velocity)…
We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way…
The discretization of fluid-poromechanics systems is typically highly demanding in terms of computational effort. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral…
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…
In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…
We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
Accurate performance estimation of future many-node machines is challenging because it requires detailed simulation models of both node and network. However, simulating the full system in detail is unfeasible in terms of compute and memory…
One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…
It is true that different approaches have been utilised to accelerate the computation of discrete logarithm problem on elliptic curves with Pollard's Rho method. However, trapping in cycles fruitless will be obtained by using the random…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…