Related papers: An Efficient Algorithm for Solving the Phase Field…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
We present maximally-fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time-step $\Delta t=A t_s^{2/3}$. For non-conserved systems, only effectively finite timesteps are…
We introduce a phase-field crystal model that creates an array of complex three- and two-dimensional crystal structures via a numerically tractable three-point correlation function. The three-point correlation function is designed in order…
We extensively study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross-Pitaevskii equation. In particular, we explore its capability of preserving a…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a ``virtual laboratory'', where materials could be designed from first-principles without relying on…
An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The…
In this work, we establish the maximal $\ell^p$-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order $\alpha\in(0,2)$, $\alpha\neq 1$, in time. These schemes include…
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is constructed by using the variable time-step BDF2 for the linear term…
In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our…
The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…
The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must…
We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable…
We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…