相关论文: Deriving a lattice model for neo-Hookean solids fr…

When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the…

The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the…

A variety of exotic non-fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The "standard" approach to studying these NFLs is by…

This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the…

This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…

Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory…

The Heterogeneous Multiscale Finite Element Method (FE-HMM) is a two-scale FEM based on asymptotic homogenization for solving multiscale partial differential equations. It was introduced in [W. E and B. Engquist, \emph{Commun. Math. Sci.},…

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…

We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary…

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…

Recent years have seen growing application potential for Lattice-skin Plate Structures in advanced manufacturing fields such as aerospace and automotive engineering. For multiscale performance evaluation of such structures, conventional…

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…

In this article, we present a new unified finite element method (UFEM) for simulation of general Fluid-Structure interaction (FSI) which has the same generality and robustness as monolithic methods but is significantly more computationally…

Lower limb amputees often suffer skin and tissue problems from using their prosthesis which is a challenging biomechanical problem. The finite element method (FEM) has previously been applied to analyse internal mechanical conditions of the…

Finite element exterior calculus (FEEC) has been developed as a systematical framework for constructing and analyzing stable and accurate numerical method for partial differential equations by employing differential complexes. This paper is…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

In this paper a problem of numerical simulation of hydraulic fractures is considered. An efficient algorithm of solution is proposed for the plain strain model of hydraulic fracturing. The algorithm utilizes a FEM based subroutine to…