Related papers: The Boundary Element Method of Peridynamics
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated. Biological organs are assumed to follow linear elastostatic material behavior, and constant boundary element is…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
This article describes a numerical method based on the dual reciprocity boundary elements method (DRBEM) for solving some well-known nonlinear parabolic partial differential equations (PDEs). The equations include the classic and…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological,…
The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently compute the electric field at arbitrary points in space. A…
We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions and computing them by fast Fourier transform (FFT), we reduce the computational complexity of PD…
We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order in time partial integro-differential equation. In this paper, we consider a nonlinear model of peridynamics in a two-dimensional spatial domain. We…
Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…