There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

비만아 부모의 돌봄 경험: q 방법론

Finite element methods for Maxwell's equations.

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

In order to maximize the performance of subsurface radar investigations, there exists a vast range of algorithms that can be applied to the data obtained to find the target's location and reflectivity. Minimizing the data computing time becomes the primary issue in choosing one algorithm over another. In this work, three imaging methods are used to reconstruct the geometric and dielectric characteristics of buried cylinders. The subject of this work is qualitative comparisons between these methods based on different performance parameters with respect to the discrepancy between calculated and true object characteristics. These methods are applied to the detection of inclusions in concrete structures.

In the Use of Parametric and Non Parametric Algorithms for the Non Destructive Evaluation of Concrete Structures

A new approach to implement a surface impedance boundary condition (SIBC) for the FDTD method Is proposed. The explicit FDTD formulation for the boundary cell closest to the surface of a conducting body is obtained using the perturbation technique in the small parameter proportional to the ratio of the values of the electric field at the opposite sides of the cell. The condition of applicability of the technique is obtained. It is shown that an FDTD code where the PEC-condition has been already implemented can be easily upgraded using the proposed technique to take into account properties of the conducting medium and improve accuracy of the computation. Numerical examples are included to illustrate the theory.

Use of the perturbation technique for implementation of surface impedance boundary conditions for the FDTD method

This paper discusses a p-adaptive finite element method for electrostatic force and energy computation based on the constitutive error criterion, and the implementation on a three-dimensional mixed polyhedral grid. The method is applied to simple MEMS structures and the convergence characteristic is demonstrated.

Three-dimensional p-adaptive computation of electrostatic force and energy

The success of two-dimensional eddy current models for modeling a variety of important nondestructive testing situations has been reported elsewhere1-3. These models, based on the finite element method, are limited to two-dimensional and axisymmetric geometries but, nevertheless are quite capable of providing important data for many practical test geometries which can be approximated by 2-D or axisymmetric formulations. The general NDT problem, is, however, a true three-dimensional problem and must be modeled as such. A 3-D eddy current model is, therefore, a natural and obvious extension of the 2-D modeling capabilities available today. Such a model is particularly valuable since the interaction between applied fields, induced currents and complicated material discontinuities cannot be described by closed form equations nor can they be approximated by 2-D geometries. In addition, such situations cannot be replicated experimentally and, therefore, the numerical model is in many cases the only practical way to provide training data for signal processing equipment and algorithms and indeed, the only way to determine defect characterization parameters to aid in the design of eddy current probes and testing equipment.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2359&context=qnde

Development of A 3-D Eddy Current Model for Nondestructive Testing Phenomena

Several second order edge elements have been applied to solving magnetostatic problems. The performances of these elements are compared through an example of magnetic circuit. In order to ensure the compatibility of the system equations and hence the convergence, the current density is represented by the curl of a source field. This avoids an explicit gauge condition which is cumbersome in the case of high order elements.

Nathan Ida

Papers

In the Use of Parametric and Non Parametric Algorithms for the Non Destructive Evaluation of Concrete Structures

Use of the perturbation technique for implementation of surface impedance boundary conditions for the FDTD method

Three-dimensional p-adaptive computation of electrostatic force and energy

Development of A 3-D Eddy Current Model for Nondestructive Testing Phenomena

Computation of magnetostatic field using second order edge elements in 3D