In this paper, we consider a priori and posteriori error estimates of the H (curl 2 )-conforming finite element when solving quad-curl eigenvalue problem. An estimate eigenvalues with convergence order 2( s − 1) is obtained if corresponding eigenvector u ∈ 1 (Ω) ∇ × (Ω). For estimate, by analyzing associated source problem, obtain lower upper bounds for errors eigenvectors in energy norm eigenv...

Decomposition of information flow associated with random threshold network dynamics on random networks with specified degree distributions is studied by numerical simulation. Combinatorial Hodge theory enables us to orthogonally decompose information flow into gradient (unidirectional acyclic flow), harmonic (global circular flow) and curl (local circular flow) components. We show that in-degre...

The paper deals with Div-Curl approximation problem by weighted thin plate splines. The weighted thin plate splines are an extension of the well known thin plate splines and are radial basis functions which allow the approximation and interpolation of a scalar functions from a given scattered data. We show how the weighted thin plate splines may also be used for the approximation and interpolat...

We explicitly introduce and exploit div-curl Young measures to examine optimal design problems governed by a linear state law in divergence form. The cost is allowed to depend explicitly on the gradient of the state. By means of this family of measures, we can formulate a suitable relaxed version of the problem, and, in a subsequent step, put it in a similar form as the original optimal design ...

This paper reports a lateral CMOS-MEMS accelerometer with a measured noise floor of 1mG/ and a dynamic range larger than 13G. The accelerometer is fully compatible with conventional CMOS processes enabling the integration of most of the conditioning circuits. It is fabricated in a three metal layer 0.5μm CMOS process followed by a two-step dry etch release. An improved curl matching technique i...

In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we exten...

We investigate the finite element methods for solving time-dependent Maxwell equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral domains. Both matching and nonmatching finite element meshes on the interfaces are considered, and optimal error estimates for both cases are obtained. The analysis of the latter case is based on an abstract framework for nested...

We study the stability of the perfectly matched layer (PML) for symmetric second order hyperbolic partial differential equations on the upper half plane, with boundary conditions at y = 0. Using a mode analysis, we develop a technique to analyze the stability of the corresponding initial boundary value problem on the half plane. We apply our technique to the PML for the elastic wave equations s...

Study of the dynamics of automorphisms of a group is usually focused on their growth and/or finite orbits, including fixed points. In this paper, we introduce properties of a different kind; using somewhat informal language, we call them metric properties. Two principal characteristics of this kind are called here the “curl” and the “flux”; there seems to be very little correlation between thes...

A novel higher order large-domain hierarchical finite-element technique using curl-conforming vector basis functions constructed from standard Legendre polynomials on generalized curvilinear hexahedral elements is proposed for electromagnetic modeling. The technique combines the inherent modeling flexibility of hierarchical elements with excellent orthogonality and conditioning properties of Le...