相关论文: Using the RD rational Arnoldi method for exponenti…
We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t.…
In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…
Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations…
We present a parallel computation scheme based on the Arnoldi algorithm for exact diagonalization of quantum-electron models. It contains a selective data transferring method and distributed storage format for efficient computing of the…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach,…
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…
We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…
Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion…
In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the…
Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for…
The low-rank alternating direction implicit (ADI) method is an efficient and effective solver for large-scale standard continuous-time algebraic Riccati equations that admit low-rank solutions. However, the existing low-rank ADI algorithm…
We consider the discretization of parabolic initial boundary value problems by finite element methods in space and a Runge-Kutta time stepping scheme. Order optimal a-priori error estimates are derived in an energy-norm under natural…
In this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on $\mathbb{R}^N$. These extremal functions minimize the $L^1(\mathbb{R}^N, |x|^{2\nu + 2 - N}dx)$-distance to the original…
This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the…