Jonatan Aronsson

Using a priori Information for Regularization in Breast Microwave Image Reconstruction

Regularization methods are used in microwave image reconstruction problems, which are ill-posed. Traditional regularization methods are usually problem-independent and do not take advantage of a priori information specific to any particular imaging application. In this paper, a novel problem-dependent regularization approach is introduced for the application of breast imaging. A real genetic algorithm (RGA) minimizes a cost function that is the error between the recorded and the simulated data. At each iteration of the RGA, a priori information about the shape of the breast profiles is used by a neural network classifier to reject the solutions that cannot be a map of the dielectric properties of a breast profile. The algorithm was tested against four realistic numerical breast phantoms including a mostly fatty, a scattered fibroglandular, a heterogeneously dense, and a very dense sample. The tests were also repeated where a 4 mm × 4 mm tumor was inserted in the fibroglandular tissue in each of the four breast types. The results show the effectiveness of the proposed approach, which to the best of our knowledge has the highest resolution amongst the evolutionary algorithms used for the inversion of realistic numerical breast phantoms.

Low-Frequency MLFMA on Graphics Processors

A parallelization of the low-frequency multilevel fast multipole algorithm (MLFMA) for graphics processing units (GPUs) is presented. The implementation exhibits speedups between 10 and 30 compared to a serial CPU implementation of the algorithm. The error of the MLFMA on the GPU is controllable down to machine precision. Under the typical method-of-moments (MoM) error requirement of three correct digits, modern GPUs are shown to handle problems with up to 7.5 million degrees of freedom in dense matrix approximation.

A Novel Skin-Effect Based Surface Impedance Formulation for Broadband Modeling of 3-D Interconnects With Electric Field Integral Equation

The problem of interconnect modeling embedded in multilayered substrate is initially formulated in terms of the volume integral equation (IE) with respect to 3-D conduction current density. One out of three degrees of freedom in volumetric current variation is then eliminated by approximating the current behavior over the coordinate normal to the conductor surface according to the skin-effect. The remaining two degrees of freedom in the volumetric current variation constitute the unknown current distribution on the conductor surface for which a governing surface electric field integral equation is obtained directly from the volume IE via restriction of the volumetric operators range to the conductor surface. The resultant surface IE features a global to the conductor cross section surface impedance operator, which is shown to approximate the relationship between tangential electric and magnetic field components on the conductor surface. The proposed novel surface IE featuring multilayered media dyadic Greens function is amenable to various discretization schemes including the Rao-Wilton-Glisson method of moments. In this paper the latter is implemented by casting the scattered field operator into Michalski-Zhengs mixed-potential form in conjunction with enforcement of global relationships between the basis and testing functions in conductor cross sections according to the surface impedance operator. Numerical comparisons to alternative conductor loss models show that the method achieves volumetric solution accuracy within the framework of a boundary-element formulation.

On the Equivalence of RWG Method of Moments and the Locally Corrected Nyström Method for Solving the Electric Field Integral Equation

The first-order locally corrected Nyström (LCN) method for the electric field integral equation is modified to ensure continuity of the current between triangular elements of the mesh. Rao-Wilton-Glisson (RWG) basis functions are used to create a conversion matrix from the LCN representation of the current to the RWG method-of-moments (MoM) representation of the current in order to enforce continuity of current between adjacent triangular flat patches. Benefits of the method are two fold: first, it provides 4 × reduction in degrees of freedom and removes unacceptable error levels in first-order LCN implementations, second, the method can be viewed as a point-based discretization of the RWG MoM offering improved efficiency in its acceleration with the fast multipole algorithm.

Error Controllable Solutions of Large-Scale Problems in Electromagnetics: MLFMA-Accelerated Locally Corrected Nyström Solutions of CFIE in 3D [Open Problems in CEM]

This work provides an overview of a parallel, high-order, error-controllable framework for solving large-scale scattering problems in electromagnetics, as well as open problems pertinent to such solutions. The method is based on the higher-order locally corrected Nystrom (LCN) discretization of the combined-field integral equation (CFIE), accelerated with the error-controlled Multi-Level Fast Multipole Algorithm (MLFMA). Mechanisms for controlling the accuracy of calculations are discussed, including geometric representation, stages of the locally corrected Nystrom method, and the MLFMA. Also presented are the key attributes of parallelization for the developed numerical framework. Numerical results validate the proposed numerical scheme by demonstrating higher-order error convergence for smooth scatterers. For the problem of scattering from a sphere, the developed numerical solution is shown to have the ability to produce a solution with a maximum relative error of the order 10-9. Open-ended problems, such as treatment of general scatterers with geometric singularities, construction of well-conditioned operators, and current challenges in development of fast iterative and direct algorithms, are also discussed.

The Barnes–Hut Hierarchical Center-of-Charge Approximation for Fast Capacitance Extraction in Multilayered Media

The Barnes-Hut algorithm is widely used in astrophysics for solving large gravitational N -body problems using O(N logN) time and memory. This reduction in computational cost is achieved by a hierarchical application of the classical center-of-mass approximation. As both gravitational and electrostatic potentials are subject to a 1/R dependence, the Barnes-Hut algorithm is also a natural choice for rapidly evaluating interactions between charged particles. The contribution of this paper is an extension of the Barnes-Hut hierarchical clustering to the acceleration of charge interactions in stratified media. We derive and validate a closed-form expression for the shift of the center-of-charge location induced by the physical inhomogeneities and show that proper positioning of the center-of-charge ensures O(1/R 3) error decay in the field approximation. Hierarchical applications of the proposed clustering approximation is demonstrated for the construction of O(N logN) method-of-moment based capacitance extractors.

A Well-Conditioned Non-Iterative Approach to Solution of the Inverse Problem

A novel methodology leading to well-conditioned formulation of the inverse scattering problem is proposed. The solution of the inverse scattering problem is made possible through elimination of the inherent ill-posedness of the inverse source problem. The latter is achieved by staging of the imaging experiment in a medium with the Greens function exhibiting focusing properties. The method is shown to cast the inverse source problem into a well-conditioned matrix equation without addition of the non-physical regularization term to the pertinent integral equation. This is contrary to the conventional iterative optimization-like methods applied to regularized integral equation with non-directional Greens function. The method is shown to be applicable in both traditional diffraction limited imaging where the evanescent waves do not participate in the information transfer from the object to the observation region as well as in the metamaterial media where focusing goes beyond the diffraction limit with the aid of the evanescent wave propagation. The diffraction limited imaging prototype is implemented using a parabolic reflector providing desired focusing properties of the Greens function. The Raleigh criteria for diffraction limited resolution is revisited to demonstrate that upon availability of the medium providing sufficient focusing properties the resolution in the conventional diffraction limited microwave tomography can go up to half-wavelength. The implementation of algorithm in medium supporting evanescent wave propagation is demonstrated using the focusing Greens function of the Veselago lens.

Exact Relationship Between the Locally Corrected Nyström Scheme and RWG Moment Method for the Mixed-Potential Integral Equation

The exact relationship between the Rao-Wilton-Glisson (RWG) method of moments (MoM) and the locally corrected Nyström (LCN) method for the mixed-potential (MP) electric field integral equation (EFIE) is presented as an extension to our work where we established analogous exact relationship for solving the EFIE in its vector-potential (VP) form. It is shown that in order to achieve one such relationship for the MP EFIE, the first- and zeroth-order LCN methods must be, respectively, used for the discretization of the VP and scalar-potential terms of the MP EFIE. The resulting numerical scheme is a point-based RWG MoM discretization of the MP EFIE via the Nyström method. Due to the MP formulation of the EFIE, the proposed method establishes notably higher accuracy compared to either RWG MoM or LCN discretizations of the EFIE in the VP form. The increased accuracy is attributed to the analytical cancellation of the line charge contributions in the MP formulation as opposed to numerical cancellation inherent in the VP formulation of the EFIE. The detailed study and explanations of the above cancellations is presented along with their impact on the accuracy of the respective schemes for both canonical and realistic scattering targets at different frequencies.

Vectorial Low-Frequency MLFMA for the Combined Field Integral Equation

A vectorial Low-Frequency Multi-Level Fast Multipole Algorithm (LF-MLFMA) is proposed for acceleration of interactions resultant from the method of moments (MoM) discretization of the combined field integral equation (CFIE). The derivatives relating the scalar Greens function to its dyadic counterparts are defined via recursive identities for scalar wave functions. The method evaluates the matrix vector product in MoM by performing three scalar LF-MLFMA passes. It is demonstrated to be stable for scatterers spanning up to 110 wavelengths in size. As the method does not impose any restrictions on the depth of the MLFMA tree, it is suitable for the solution of both broadband and multiscale problems.

Solution of large multiscale EMC problems with method of moments accelerated via low-frequency MLFMA

The paper demonstrates that for large-scale electromagnetic compatibility problems not exceeding 120λ in size the low-frequency-multilevel-fast-multipole-algorithm (LF-MLFMA) based on spherical wave function expansions is advantageous to its high-frequency counterpart based on plane wave expansions. In the latter the depth of the tree is restricted by the smallest size of the leaf-level box size of 0.1λ making it inefficient at either low-frequencies or for problems with multi-scale features. The low-frequency MLFMA, however, has no limitation on the depth of the tree and allows for full-wave acceleration of Moment Method from DC to frequencies at which the models spans up to 120λ. Such broadband behaviour of the low-frequency MLFMA is made possible through construction of numerically stable translation operators for the spherical wave functions with orders reaching 180. This paper provides an overview of the algorithms allowing for stable high order translations of spherical functions. The LF-MLFMA accelerated Rao-Wilton-Glisson Moment Method utilizing one such algorithm is demonstrated in the frequency range from 1MHz to 2.5GHz for the problem of plane wave coupling to antennas onboard the F5 fighter jet at fixed discretization featuring 2 million surface elements.