Related papers: An unfitted radial basis function generated finite…
Motion estimation of organs in a sequence of images is important in numerous medical imaging applications. The focus of this paper is the analysis of 4D Respiratory Correlated Computed Tomography (RCCT) Imaging. It is hypothesized that the…
The temporal interpolation task for 4D medical imaging, plays a crucial role in clinical practice of respiratory motion modeling. Following the simplified linear-motion hypothesis, existing approaches adopt optical flow-based models to…
The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…
Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces…
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
In our earlier work, we proposed a data-driven filtered reduced order model (DDF-ROM) framework for the numerical simulation of fluid flows, which can be formally written as \begin{equation*} \boxed{ \text{ DDF-ROM = Galerkin-ROM +…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the…
In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an…
We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with…
Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive…
The present work deals with the numerical resolution of coupled 3D-2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model,…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the…
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation uses an RBF discretization in space and finite differences in…