相关论文: A general-purpose element-based approach to comput…
We evaluated the performance of the classical and spectral finite element method in the simulation of elastodynamic problems. We used as a quality measure their ability to capture the actual dispersive behavior of the material. Four…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…
The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
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…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
It is common for dispersion curves of damped periodic materials to be based on real frequencies versus complex wavenumbers or, conversely, real wavenumbers versus complex frequencies. The former condition corresponds to harmonic wave motion…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
Summary This work presents variational concepts associated with reduced Trefftz type approaches and discusses the interrelationship between various concepts of the displacement, hybrid and Trefftz methods. The basic concept of the…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
The periodic cellular topology characterizing the microscale structure of a heterogeneous material may allow the finest functional customization of its acoustic dispersion properties. The paper addresses the free propagation of elastic…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
Dispersion diagrams play a crucial role in examining, analyzing and designing wave propagation in periodic structures. Despite their ubiquity and current research interest, introductory papers and reference scripting tailored to novel…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…