相关论文: Higher-Order Deflation for Polynomial Systems with…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
We consider the solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order (HHO) methods. The two resulting second-order elliptic problems can be decoupled via the introduction of a new unknown, corresponding to…
We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that an operator deduced by adding $Df(x)$ and a projection of $D^2f(x)$ in a direction of the kernel of $Df(x)$ is…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an algorithm for computing the multiplicity structure, proposes…
In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution…
This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. On the basis of the truncation method, an algorithm for numerical differentiation is constructed, which is…
The numerical integration of an analytical function $f(x)$ using a finite set of equidistant points can be performed by quadrature formulas like the Newton-Cotes. Unlike Gaussian quadrature formulas however, higher-order Newton-Cotes…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…