相关论文: An Efficient Algorithm for Solving the Phase Field…

We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…

We propose two easy-to-implement fast algorithms based on moment-matching to compute the nonlocal potential $\varphi(\textbf{x})=(U\ast \rho)(\textbf{x})$ on bounded domain, where the kernel $U$ is singular at the origin and the density…

Kalman Filter (KF) is an optimal linear state prediction algorithm, with applications in fields as diverse as engineering, economics, robotics, and space exploration. Here, we develop an extension of the KF, called a Pathspace Kalman Filter…

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…

This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based…

We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse…

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…

Crystal structure prediction (CSP) is crucial for identifying stable crystal structures in given systems and is a prerequisite for computational atomistic simulations. Recent advances in neural network potentials (NNPs) have reduced the…

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media properties. It requires very small time step size to perform…

We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…

In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…

We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…

We present a computational framework for piecewise constant functions (PCFs) and use this for several types of computations that are useful in statistics, e.g., averages, similarity matrices, and so on. We give a linear-time,…

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field…

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…

We propose a novel approach to continuum modelling of dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…

State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which…

Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…