Related papers: A fast immersed boundary method for an extruded wa…
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
A parallel dynamic overset framework has been developed for the curvilinear immersed boundary (overset-CURVIB) method to enable tackling a wide range of challenging flow problems. The dynamic overset grids are used to locally increase the…
This work addresses a novel version of the kernel-free boundary integral (KFBI) method for solving elliptic PDEs with implicitly defined irregular boundaries and interfaces. We focus on boundary value problems and interface problems, which…
We present the implementation and validation of an immersed boundary volume penalization method in the computational fluid dynamics solver CODA (from ONERA, DLR, and Airbus). Our goal is to model and simulate turbulent fluid flows in…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically…
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…
A novel sharp interface ghost-cell based immersed boundary method has been proposed and its parameters have been optimized against an analytical model in diffusion applications. The proposed embedded constrained moving least-squares (ECMLS)…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
In the lattice Boltzmann method (LBM), the widely utilized wall boundary is the bounce-back (BB) boundary, which corresponds to the no-slip boundary. The BB boundary prevents the LBM from capturing the accurate shear drag on the wall when…
The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender…
Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate in the velocity. However, almost no rigorous theoretical…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…
In this paper we employ two implementations of the fictitious domain (FD) method to simulate water-entry and water-exit problems and demonstrate their ability to simulate practical marine engineering problems. In FD methods, the fluid…
The transparent boundary condition for the free Schr\"{o}dinger equation on a rectangular computational domain requires implementation of an operator of the form $\sqrt{\partial_t-i\triangle_{\Gamma}}$ where $\triangle_{\Gamma}$ is the…