相关论文: Parareal algorithm via Chebyshev-Gauss spectral co…
We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treating the potential in an extended window for its discrete…
A high-order convergent numerical method for solving linear and non-linear parabolic PDEs is presented. The time-stepping is done via an explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method of order 4 or 5, and for the implicit…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput.…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) =…
This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
The PC algorithm uses conditional independence tests for model selection in graphical modeling with acyclic directed graphs. In Gaussian models, tests of conditional independence are typically based on Pearson correlations, and…
We present a Chebyshev collocation method for linear ODE and DDE problems. We first give a posteriori estimates for the accuracy of the approximate solution of a scalar ODE initial value problem. Examples of the success of the estimate are…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
This paper is dedicated to enhancing the computational efficiency of traditional parallel-in-time methods for solving stochastic initial-value problems. The standard parareal algorithm often suffers from slow convergence when applied to…
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…