Related papers: Convergence of a Fast Explicit Operator Splitting …
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
We present an operator-splitting scheme for fluid-structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear…
In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…
This work addresses computing techniques for dose calculations in treatment planning with proton and ion beams, based on an efficient kernel-convolution method referred to as grid-dose spreading (GDS) and accurate heterogeneity-correction…
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also…
Reconfigurable intelligent surfaces (RISs) are often assumed to allow continuous phase control over all elements, leading to hardware cost that scales with the number of elements. Treating the phase of each element as a discrete variable is…
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…
The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…
Spectrally and energy efficient orthogonal frequency division multiplexing (SEE-OFDM) is an optical OFDM technique based on combining multiple asymmetrically clipped optical OFDM (ACO-OFDM) signals into one OFDM signal. By summing different…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…
The main difficulty in studying numerical method for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (J. Printems. [ESAIM Math. Model. Numer. Anal. (2001)]). Although fruitful results on numerical…
We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable $U$ in…
Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…