6 citations · 19 across the 14 of their papers we have counts for
16 papers
Symplectic Discretization Approach for Developing New Proximal Point Algorithm
Ya-xiang Yuan, Yi Zhang
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the…
A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions
Yi Zhang, Artur Palha, Marc Gerritsma +1
In this work, we introduce a mass, energy, enstrophy and vorticity conserving (MEEVC) mixed finite element discretization for two-dimensional incompressible Navier-Stokes equations…
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
Nobuki Takayama, Takaharu Yaguchi, Yi Zhang
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve…
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains
Yi Zhang, Artur Palha, Marc Gerritsma +1
We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization…
Computing differential Galois groups of second-order linear -difference equations
Carlos E. Arreche, Yi Zhang
We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear -difference…
A conservative hybrid method for Darcy flow
Varun Jain, Yi Zhang, Joël Fisser +2
We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for 1) conservation of mass, and 2) inter-element continuity, are topological…
Fully Discrete Mixed Finite Element Methods for the Stochastic Cahn-Hilliard Equation with Gradient-type Multiplicative Noise
Xiaobing Feng, Yukun Li, Yi Zhang
This paper develops and analyzes some fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise that is white in…
Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Non-central Wishart Matrix
Nobuki Takayama, Lin Jiu, Satoshi Kuriki +1
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The fo…
Rational Solutions of First-Order Algebraic Ordinary Difference Equations
Thieu N. Vo, Yi Zhang
We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary…
Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise
Xiaobing Feng, Yukun Li, Yi Zhang
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The n…
Algebraic dual polynomials for the equivalence of curl-curl problems
Marc Gerritsma, Varun Jain, Yi Zhang +1
In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity and one problem for a vector field . For Dirichlet…
On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Sebastian Falkensteiner, Yi Zhang, Thieu N. Vo
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solu…
Mimetic Spectral Element Method for Anisotropic Diffusion
Marc Gerritsma, Artur Palha, Varun Jain +1
This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discusse…
Construction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshes
Varun Jain, Yi Zhang, Artur Palha +1
Given a sequence of finite element spaces which form a de Rham sequence, we will construct a dual representation of these spaces with associated differential operators which connec…
Rational Solutions of High-Order Algebraic Ordinary Differential Equations
Thieu N. Vo, Yi Zhang
We consider algebraic ordinary differential equations (AODEs) and study their polynomial and rational solutions. A sufficient condition for an AODE to have a degree bound for its p…
Apparent Singularities of D-finite Systems
Shaoshi Chen, Manuel Kauers, Ziming Li +1
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characteriz…