Junqing Chen

An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings

We develop an adaptive finite element method for solving the eddy current model with voltage excitations for complicated three-dimensional structures. The mathematical model is based on the

AN ADAPTIVE PERFECTLY MATCHED LAYER TECHNIQUE FOR 3-D TIME-HARMONIC ELECTROMAGNETIC SCATTERING PROBLEMS

\mathbf{A}-\phi

Reverse time migration for extended obstacles: electromagnetic waves

formulation whose well-posedness is established. We derive the a posteriori error estimate for the finite element approximation of the model whose solution is not unique in the nonconducting region. Numerical experiments that illustrate the competitive behavior of the proposed method are provided.

Reverse time migration for extended obstacles: acoustic waves

An adaptive perfectly matched layer (PML) technique for solving the time harmonic electromagnetic scattering problems is developed. The PML parameters such as the thickness of the layer and the fictitious medium property are determined through sharp a posteriori error estimates. Combined with the adaptive finite element method, the adaptive PML technique provides a complete numerical strategy to solve the scattering problem in the framework of FEM which produces automatically a coarse mesh size away from the fixed domain and thus makes the total computational costs insensitive to the thickness of the PML absorbing layer. Numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method.

Accelerated floating random walk algorithm for the electrostatic computation with 3-D rectilinear-shaped conductors

We propose a new single-frequency reverse time migration (RTM) algorithm for imaging extended targets using electromagnetic waves. The imaging functional is defined as the imaginary part of the cross-correlation of the Green function for the Helmholtz equation and the back-propagated electromagnetic field. The resolution of our RTM method for both penetrable and non-penetrable extended targets is studied by virtue of the Helmholtz?Kirchhoff identity for the time-harmonic Maxwell equation. The analysis implies that our imaging functional is always positive and thus may have better stability properties. Numerical examples are provided to demonstrate the powerful imaging quality and confirm our theoretical results.

Detection and classification from electromagnetic induction data

We consider the resolution of the single-frequency reverse time migration method for extended targets without the assumption of the validation of the geometric optics approximation. The resolution analysis, which applies in both penetrable and non-penetrable obstacles with sound soft or impedance boundary condition on the boundary of the obstacle, implies that the imaginary part of the cross-correlation imaging functional is always positive and thus may have better stability properties. Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.

An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements

Abstract With the advancement of fabrication technology, the electrostatic coupling has increasing impact on the performance of very large-scale integrated (VLSI) circuits and micro-electromechanical systems (MEMS). For the structures in VLSI circuits which are mostly rectilinear geometries, the floating random walk (FRW) method using cubic transition domains has been successfully applied to calculate the electric capacitances among interconnect wires. In this work, the techniques of importance sampling and stratified sampling are presented to accelerate the FRW algorithm by improving the convergence rate of the Monte Carlo procedure. An efficient approach is then presented to parallelize the FRW algorithm with the graphic processing units (GPUs). GPU-friendly algorithmic flow and data structure are designed to reduce the divergence among random walks and the time of accessing the device memory. The presented techniques are also applicable to the calculation of electric field intensity, which is also an important problem for nowadays nanometer-technology circuits. Numerical results are presented with several simple structures and larger ones from real VLSI circuits or MEMS. The results validate the accuracy of the presented techniques and demonstrate up to 100× speedup due to the variance reduction and GPU-based parallel computing.

Convergence analysis of an adaptive edge element method for Maxwell's equations

In this paper we introduce an efficient algorithm for identifying conductive objects using induction data derived from eddy currents. Our method consists of first extracting geometric features from the induction data and then matching them to precomputed data for known objects from a given dictionary. The matching step relies on fundamental properties of conductive polarization tensors and new invariance properties introduced in this paper. A new shape identification scheme is developed and tested in numerical simulations in the presence of measurement noise. Resolution and stability properties of the proposed identification algorithm are investigated.

Target detection and characterization from electromagnetic induction data

We propose and analyze an adaptive inverse iterative method for solving the Maxwell eigenvalue problem with discontinuous physical parameters in three dimensions. The adaptive method updates the eigenvalue and eigenfunction based on an a posteriori error estimate of the edge element discretization. At each iteration, the involved saddle-point Maxwell system is transformed into an equivalent system consisting of a singular Maxwell equation and two Poisson equations, for both of which preconditioned iterative solvers are available with optimal convergence rate in terms of the total degrees of freedom. Numerical results are presented, which confirms the quasi-optimal convergence of the adaptive edge element method in terms of the numerical accuracy and the total degrees of freedom.