M. Y. Xia

Stable Electric Field TDIE Solvers via Quasi-Exact Evaluation of MOT Matrix Elements

Prior theoretical studies and experience confirm that the stability of marching-on-in-time (MOT) solvers pertinent to the analysis of scattering from free-standing three-dimensional perfect electrically conducting surfaces hinges on the accurate evaluation of MOT matrix elements resulting from a Galerkin discretization of the underlying time domain integral equation (TDIE). Unfortunately, the accurate evaluation of the four-dimensional spatial integrals involved in the expressions for these matrix elements is prohibitively expensive when performed by computational means. Here, a method that permits the quasi-exact evaluation of MOT matrix elements is presented. Specifically, the proposed method permits the analytical evaluation of three out of the four spatial integrations, leaving only one integral to be evaluated numerically. Since the latter has finite range and a piecewise smooth integrand, it can be evaluated to very high accuracy using standard quadrature rules. As a result, the proposed method permits the fast evaluation of MOT matrix elements with arbitrary (user-specified) accuracy. Extensive numerical experiments show that an MOT solver for the electric field TDIE that uses the proposed quasi-exact method is stable for a very wide range of time step sizes and yields solutions that decay exponentially after the excitation vanishes.

Numerical Analysis of Scattering by Dielectric Random Rough Surfaces Using Modified SMCG Scheme and Curvilinear RWG Basis Functions

An augmented sparse-matrix canonical-grid (SMCG) approach for numerical analysis of scattering by dielectric random rough surfaces is developed. It is an extension of the previous modified SMCG scheme for perfect-electric-conducting (PEC) surfaces to dielectric cases, and is enhanced by adopting curved triangulation modeling. By using the curved modeling with curvilinear Rao-Wilton-Glisson basis functions (CRWG bases), the number of unknowns can be reduced substantially to extract results of the same accuracy, compared with using the planar triangular discretization with planar RWG bases. Numerical results for Gaussian and ocean-like dielectric rough surfaces are provided to confirm the validity and efficacy of the proposed method.

A stable marching-on-in-time solver for time domain surface electric field integral equations based on exact integration technique

Theoretical studies [1] and experience confirm that the stability of marching-on-in-time (MOT) solvers pertinent to the analysis of scattering from free-standing three-dimensional perfect electrically conducting (PEC) surfaces hinges on the accurate evaluation of the MOT matrix elements resulting from a Galerkin discretization of the underlying integral equation. Unfortunately, accurate evaluation of the four-dimensional spatial integrals called for is prohibitively expensive when performed by numerical means. To mitigate this cost, in [2] two-dimensional integrals over source coordinates are evaluated analytically while the remaining two-dimensional integration over testing coordinates is carried out numerically; the technique in [2] assumes the use of Rao-Wilton-Glisson (RWG) spatial basis functions [3] and Lagrange polynomial temporal expansions [4]. While the MOT solver in [2] was shown to be stable for a wide range of problems involving up to 50,000 time steps, subsequent studies have revealed instabilities for small time steps.

An enhanced TDIE solver using causal-delayed temporal basis functions and curvilinear RWG spatial basis functions

An enhanced time domain integral equation (TDIE) solver is proposed for analysis of transient scattering problems. It entails the use of causal-delayed temporal basis functions and curvilinear Rao-Wilton-Glisson (RWG) basis functions, both of which have the potential to reduce the number of unknowns. The causal-delayed temporal basis functions have twofold effects: one is causally to eliminate the spurious solutions created before the incident wave arrives, and the other is dynamically to extract the phase variations of the induced currents on the scatterer. The curvilinear triangular patches can increase the modeling precision than the planar ones. Numerical results show that, a combined use of the improved temporal and spatial basis functions can greatly reduce the number of unknowns and thus save the core memory resource and computing time for general 3D bodies.

Time domain integral equation solvers using curvilinear RWG spatial basis functions and quadratic B-spline temporal basis functions

In this paper, a robust TDIE solver based on using the quadratic B-spline temporal basis functions and curvilinear RWG spatial basis functions for transient scattering problems by arbitrarily-shaped bodies, including tapering ones, is presented. The MOT solutions converge at exponential rate at early time and then level off at machine precision, which demonstrates wonderful stability and accuracy.

Parametric geometric modeling using piecewise interpolation functions for solutions of electromagnetic integral equations

A parametric geometric modelling method for solution of electromagnetic integral equations that employs piecewise Lagrange polynomials that use only partial interpolation nodes to fit the curved surfaces, other than higher-order Lagrange interpolation that involves all nodes, is proposed. The method has compact formulae for arbitrary order, and is flexible to be combined with curved quadrilateral and triangular basis functions. Its correctness and efficacy are confirmed by applying it to the simulation of rough surface scattering using the modified Sparse-Matrix Canonical-Grid (SMCG) method.

Simulation of transient scattering from ocean surface with ship wake

A time domain integral equation (TDIE) based procedure for simulation of transient scattering from ocean surface with ship wake is developed. First, the simulated surface is generated by using the ocean power spectrum and the ship spectrum. Smoothing technique is used to handle the truncated boundary. Then the TDIE method is employed to extract the backscattered signatures. Doppler spectrum is analyzed by using the time domain echoes. Numerical examples are provided to validate the proposed scheme.

A Probabilistic Model for the Nonlinear Electromagnetic Inverse Scattering: TM Case

Electromagnetic inverse scattering (EMIS) is a noninvasive examination tool, which holds the promising potential in science, engineering, and military applications. In contrast to conventional tomography techniques, the inverse scattering is a quantitative superresolution imaging method since it is capable of accommodating more realistic interactions between the wavefield and the probed scene. In this paper, a full probabilistic formulation of the EMIS is presented for the first time, which is then solved by applying the well-known expectation maximization method. Afterward, the concept of the complex-valued alternating direction method of multipliers has been proposed as an alternative approach to solve the resulting nonlinear optimization problem. Finally, exemplary numerical and experimental results are provided to validate the proposed method.

Validation of Extended Kirchhoff Approximation and Small Slope Approximation for electromagnetic scattering from ship wake surfaces

Extended Kirchhoff approximation and small slope approximation are employed to calculate the normalized radar cross-section of ship wake surfaces. Method of moments accelerated by the multilevel fast multipole algorithm is adopted to test the accuracy of the two analytical approximate methods. Numerical results show that the two approximate approaches can extract reliable results unless at large scattering angles, which permits us to simulate the scattering from extremely large wake surfaces.

Backscattering of a hypersonic cone with plasma sheath at different attack angles

A simulation procedure to examine the backscattering radar cross-section (RCS) of a hypersonic object with plasma sheath is presented. Computational fluid dynamics tool is adopted to resolve the distributions of electron density and atmospheric temperature, and then the complex dielectric constant of plasma sheath are found. Volume-surface integral equation method is employed to extract the backscattering RCS of the hypersonic object with plasma sheath. Numerical results show that the plasma sheath can absorb some electromagnetic waves at L-band and reduce the backscattering RCS almost in any direction. Also, the attack angle of the moving object influences the backscattering RCS for both vertical and horizontal polarization incidences.