Related papers: A non-balanced staggered-grid finite-difference sc…
In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte…
The second order weighted and shifted Gr\"{u}nwald difference (WSGD) operators are developed in [Tian et al., arXiv:1201.5949] to solve space fractional partial differential equations. Along this direction, we further design a new family of…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…
In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in…
Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
The objective of this work is to investigate the utility and effectiveness of the high-order scheme for simulating unsteady turbulent flows. To achieve it, the studies were conducted from two perspectives: (i) the ability of different…
This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid framework to ensure local conservation of fluxes,…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…