相关论文: Finite Difference Weerakoon-Fernando Method to sol…
A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…
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…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
We present a gradient-based algorithm for unconstrained minimization derived from iterated linear change of basis. The new method is equivalent to linear conjugate gradient in the case of a quadratic objective function. In the case of exact…
Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We propose high-order FDTD schemes based on the Correction Function Method (CFM) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an…
In this paper, we present a new method for variable elimination in systems of inequations which is much faster than the Fourier-Motzkin Elimination (FME) method. In our method, a linear Diophantine problem is introduced which is dual to our…
In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an…
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
We introduce a new projection-free (Frank-Wolfe) method for optimizing structured nonconvex functions that are expressed as a difference of two convex functions. This problem class subsumes smooth nonconvex minimization, positioning our…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with non-smooth solution. Two popular finite…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
This article discusses a mixed FE technique for 3D nonlinear elasticity using a Hu-Washizu (HW) type variational principle. Here, the deformed configuration and sections from its cotangent bundle are taken as additional input arguments. The…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…