Yaniv Brick

Ben-Gurion University of the Negev | bgu · Department of Electrical and Computer Engineering

A hierarchical- (or $\mathcal {H}$ -) matrix fast direct solver, utilizing a generalized source integral equation (IE) for essentially convex scatterers, that is suitable for both strong and weak admissibility settings, is presented. The IE assigns to each elemental source auxiliary sources that significantly attenuate its radiation into the scat...

An integral equation formulation, using generalized directional sources, for three-dimensional scattering by impenetrable and essentially convex bodies, is presented. This formulation increases the rank-deficiency of moment matrix blocks representing interactions between non-overlapping source and observer regions. Thereby, it enables enhanced low-...

The spatial sampling and interpolation approach, facilitating construction of fast algorithms, for a variety of computational problems of computational electromagnetics and acoustics, is reviewed. Efficient sampling techniques for static and dynamic fields in near and far zones are presented and employed to construct pertinent fast field evaluation...

An easy-to-implement iterative algorithm that enables efficient and scalable spectral analysis of dense matrices is presented. The algorithm relies on the approximation of a matrix's singular values by those of a series of smaller matrices formed from uniform random sampling of its rows and columns. It is shown that, for sufficiently incoherent and...

A method for the fast computation of radiation by Gaussian windows, with controllable error, is presented. The computation aims to complement beam summation frameworks as an alternative to analytical propagators (e.g., the paraxial Gaussian beam and the complex source beam). Its accuracy in describing the off-axis fields is of particular interest f...

No PDF available ABSTRACT Reliable modeling of the scattering by acoustically large and geometrically complex objects can be achieved by means of subdomain-dependent problem formulation and a numerically rigorous solution. While the objects’ inhomogeneity has driven the development of differential equation formulations and solvers, integral equatio...

The acoustic scattering by highly inhomogeneous objects is analyzed by a method of moments solver for the volume integral equation. To enable the treatment of acoustically large scatterers of various topologies, the iterative numerical solution of the resulting system is accelerated via a kernel independent algebraic compression scheme: Blocks of t...

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large aperture...

A fast method to assess and correct the domain misrepresentation of impedance matrix blocks, Z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">os</sup> , based on their row- and column-sampling, to ensure the accuracy of their low-rank approximation (LRA), is presented. The misrepresentation arises whe...

An algorithm for the fast computation of multi-static scattering patterns, produced by low-contrast inhomogeneous volumetric objects, which satisfy the Born approximation assumption, is presented. The algorithm relies on hierarchical interpolation and aggregation of optimally sampled phase-compensated partial contributions to the scattered field in...

We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field’s phase to form smooth caustic surfaces that include the desired trajectory. The aperture ampl...

The butterfly-compressibility of moment-matrix blocks is studied quantitatively, for various geometrical configurations and compression algorithm parameters. To enable investigation of electrically large geometries, the methodology employs simplified expressions for the compressed memory and fast low-rank approximation techniques. The study indicat...

A class of inherently compressible integral equation formulations for problems of scattering by impenetrable objects, which makes use of generalized directional sources, is presented. The new formulation effectively reduces the problem’s dimensionality and, thus, allows for efficient low-rank compression of moment matrices’ off-diagonal blocks. Whe...

A physics-based rank-revealing multilevel algorithm to more efficiently compute low-rank (LR) approximations of the method of moments matrix blocks ${\mathbf{Z}}^{\textrm {os}}$ is presented. Using surface subsets of volumetric nonuniform spherical grids (proxy grids), an LR approximation ${\mathbf{Z}}^{\textrm {os}}\approx {\mathbf{AB}}^{\dagger...

The monitoring and diagnostics of induced fractures are important for the real-time performance evaluation of hydraulic fracturing operations. Previous electromagnetic-based studies show that single backbone triaxial induction logging tools are promising candidates for real-time monitoring and diagnosis of fractures in noncased wells. With a fast-f...

A shadow-radiation-based fast iterative physical optics (FIPO) scheme, for the analysis of the scattering from large complex geometries involving multiple reflection and occlusion effects, is proposed. By employing a “shadow radiation” mechanism, the scheme alleviates the need in expensive computation and storage of a geometric visibility function....

The efficiency of a hydraulic fracture treatment depends primarily on the dimensions and orientation of propped fractures. We have developed a novel electrode-based resistivity tool concept for mapping proppant distribution in hydraulic fractures in steel-cased wellbores. The proposed tool configuration is shown to overcome the severe limitations o...

Several asymptotic complexity expressions in [1] were overestimated and require correction. All the errors resulted from the same incorrect assumption: at the end of Section II, the computational complexity of calculating the singular value decomposition (SVD) of an $m \times n$ matrix ${\mathbf{A}}$ was presented as $\mathcal {O}(m^{{{{2}}}}n+n^{{...

A physics-based algorithm for accelerating the computation of method of moments matrix blocks’ low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions by using non-uniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row...

A fast algorithm for the diagnosis of large antennas is developed. The algorithm is based on the Rayleigh-Sommerfeld (RS) backpropagation method, accelerated by a multilevel nonuniform grid algorithm. Comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects a...

The implementation of a low-frequency electromagnetic induction tool for propped fracture detection and diagnostics requires an in-depth examination of the reliability and accuracy of the method across fractures with realistic geomechanical features. Likewise, the method relies on the effective placement of electrically conductive proppant within t...

Two physics-based rank-revealing multilevel algorithms are presented to efficiently compute impedance matrix blocks' low-rank representations. Both algorithms rely on non-uniform sampling of phase- and amplitude-compensated fields but use different auxiliary grids. The algorithms' computational costs and range of validity are compared.

An ℋ-matrix based fast direct solver is presented to accelerate the solution of volume integral equations pertinent to the analysis of hydraulic fracture resistivity measurements. The solvers performance for this problem type is compared to that of an FFT-accelerated iterative solver.

Different types of multiscale problems encountered in classical electromagnetics are discussed. A nomenclature is proposed that is useful for identifying the difficulty of a problem and the suitability of a computational method for solving it.

The multilevel nonuniform-grid (MLNG) algorithm, which belongs to the class of "fast" algorithms, is adapted for solving three-dimensional electromagnetic scattering problems. This makes it possible to extend the range of rigorous simulation to significantly higher frequencies and scatterer's sizes than those available for “conventional” methods.

A fast and stable boundary element method (BEM) algorithm for solving external problems of acoustic scattering by impenetrable bodies is developed. The method employs the Burton-Miller integral equation, which provides stable convergence of iterative solvers, and a generalized multilevel nonuniform grid (MLNG) algorithm for fast evaluation of field...

A fast algorithm for the evaluation of the double-bounce (DB) contributions to the physical optics scattering integrals, over a range of aspect angles and frequencies, is presented. The work extends the preceding far-field algorithm, to encompass three-dimensional and near-field scenarios. The algorithm relies on multilevel sampling and interpolati...

A novel iterative physical optics (IPO) algorithm is proposed, for the analysis of scattering from large complex geometries involving multiple reflections and complex self-shadowing effects. The algorithm involves two types of nested iterations: reflection (“bounce”) iterations and self-shadowing iterations. At each bounce iteration, the physical o...

A multilevel algorithm for the fast computation of double bounce (DB) contributions to near field (NF) scattering physical optics (PO) integrals is presented. The algorithm aims at accelerating the computation of the mono-static DB contribution for multiple excitations, i.e., for sources set within a wide range of locations with respect to the scat...

A fast algorithm for the direct solution of the method of moments (MoM) systems of equations describing scattering from essentially convex bodies is presented. The algorithm reveals the ranks of interactions between subdomains and compresses the system to that of interacting unknowns only. The procedure is facilitated by representing the interactio...

An algorithm for the fast computation of the physical optics (PO) integral describing single bounce back scattering in near-field scenarios is presented. The algorithm is based on a multilevel computation of partial contributions to the PO integral by hierarchically ordered subdomains. Phase- and amplitude-compensation of the partial contributions...

A novel simple to implement technique to accelerate the method of moments applied to surface integral equations of computational electromagnetics is presented. The method is based on the non-uniform grid algorithm and its precision is enhanced by efficient quadrature rules for the accurate computation of near-field based on the cancellation techniq...

Fast source imaging method based on Rayleigh-Sommerfeld (RS) back-propagation accelerated by multilevel nonuniform grid algorithm (MLNG) is developed. 2D sampling schemes in spherical and oblate-spheroidal coordinates are compared to the full 3D spherical scheme in terms of efficiency and accuracy. The method is evaluated on the example of a parabo...

An efficient procedure for the evaluation of the Green's function for a source and multiple observation points near a convex impedance boundary cylinder is presented. The evaluation is performed using non-uniform grids spread along the cylinder's perimeter and regionally tailored for capturing the Green's function's behavior in the line-of-sight an...

A fast algorithm for the computation of the physical optical back scattering integral is presented. The algorithm employs a multilevel evaluation scheme based on optimal sampling and restoration of partial contributions on grids tailored for near- and far-fields. Reduction of the asymptotic computational complexity by 2 polynomial orders is achieve...

A fast multilevel algorithm for the direct solution of a scattering problem, represented using the generalized field integral equation (GEIE), is presented. The algorithm exploits the inherent high rank deficiency of the GEIE to allow for a solution at a cost of O(kR) operations per excitation. The fast compression is achieved using the non-uniform...

A novel multilevel direct solver based on the recently proposed generalized equivalence integral equation (GEIE) for scattering by impenetrable essentially convex objects (A. Boag and V. Lomakin, EuCAP 2012) is presented. The solver relies on the high compressibility achievable for the discrete forms of the GEIE that are obtained, for example, via...

A novel fast direct solver using the recently proposed generalized equivalence integral equation (GEIE) is presented. By eliminating the line-of-sight between distant subdomains of convex geometries, the GEIE essentially reduces the problems' dimensionality, thus producing highly compressible impedance matrices. The compression is facilitated using...

A fast non-iterative algorithm for the solution of large 3-D acoustic scattering problems is presented. The proposed approach can be used in conjunction with the conventional boundary element discretization of the integral equations of acoustic scattering. The algorithm involves domain decomposition and uses the nonuniform grid (NG) approach for th...

An approach for the fast direct solution of scattering problems via compression of boundary element method (BEM) matrices is presented. Such an approach is advantageous for large resonant problems where iterative solvers converge poorly, or if the solutions are sought for multiple directions of incidence, so that the computational cost becomes prop...

This paper presents a software framework that allows the integration of efficient fast iterative and direct solvers with various Method of moment (MoM) engines. The idea leads to a future open-source software project to integrate modules developed by different University groups with expertise either in accurate computation of Integral Equations Gre...

An algorithm for the compression of the method of moments (MoM) matrices is presented and demonstrated for representative examples. The algorithm employs the non-uniform grid approach to reduce by a significant factor the complexity of computing interacting and non-interacting subdomain modes to be used as basis and testing transformations. Compres...

A fast algorithm for the evaluation of acoustic fields produced by given source distributions is developed with the aim of accelerating iterative boundary element method (BEM) solvers. The algorithm is based on field smoothing by phase and amplitude compensation, which allows for sampling of the fields radiated by finite-size source distributions o...

A multilevel non-uniform grid (MLNG) algorithm is used for acceleration of iterative integral equation based analysis of scattering from arbitrary shaped large bodies. The acceleration is achieved by replacing the matrix-vector products performed by an iterative method of moments (MoM) solver by an equivalent fast field evaluation via the MLNG algo...

A fast algorithm for computing the scattering cross section of arbitrary shaped large rigid bodies using an iterative method of moments solver has been presented. The main computational bottleneck of such iterative solvers stems from the need to perform at each iteration at least one matrix‐vector product. If performed directly, matrix‐vector multi...

The analysis of large scattering problems is often performed using iterative method-of-moments (MoM) solvers. The main computational bottleneck of such iterative solvers stems from the need to perform at each iteration at least one matrix-vector product, which is equivalent to field evaluation for a given source distribution. The O(N²) c...