Related papers: A fourth-order multi-scale computational method an…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…
In this paper, we give some new thoughts about the classical gradient method (GM) and recall the proposed fractional order gradient method (FOGM). It is proven that the proposed FOGM holds a super convergence capacity and a faster…
Popular machine learning approaches forgo second-order information due to the difficulty of computing curvature in high dimensions. We present FOSI, a novel meta-algorithm that improves the performance of any base first-order optimizer by…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
Fiber orientation distributions (FODs) is a popular model to represent the diffusion MRI (dMRI) data. However, imaging artifacts such as susceptibility-induced distortion in dMRI can cause signal loss and lead to the corrupted…
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
We extend the nonlocal operator method to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original nonlocal operator method proposed by the authors in [A…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized in space by finite differences. The resulting skew-gradient…
The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…
High-frequency issues have been remarkably challenges in numerical methods for partial differential equations. In this paper, a learning based numerical method (LbNM) is proposed for Helmholtz equation with high frequency. The main novelty…
The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…
We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…