SUMMARY This text introduces the following: (1) new regularized combined field integral equations (CFIE‐R) for frequency‐domain sound‐hard scattering problems; and (2) fast, high‐order algorithms numerical solution of CFIE‐R related equations. Similar to classical equation (CFIE), are uniquely‐solvable based on use single double layer potentials. Unlike CFIE, however, utilize a composition double‐layer potential with regularizing operator that gives rise highly favorable spectral...

This paper introduces a new windowed Green function (WGF) method for the numerical integral-equation solution of problems electromagnetic scattering by obstacles in presence dielectric or conducting half-planes. The WGF method, which is based on use smooth windowing functions and integral kernels that can be expressed directly terms free-space function, does not require evaluation expensive Sommerfeld integrals. proposed approach fast, accurate, flexible, easy to implement. In particular,...

Journal Article Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann conditions Get access Yassine Boubendir, Boubendir Department of Mathematical Sciences and Center Applied Mathematics Statistics, NJIT, Univ. Heights. 323 Dr. M.L. King Jr. Blvd, Newark, NJ 07102, USA Search other works by this author on: Oxford Academic Google Scholar Catalin Turc * *Corresponding authors: catalin.c.turc@njit.eduboubendir@njit.edu IMA...

We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains corners.We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) whose name reflects that (1) they consist combinations equations second-kind first-kind which are preconditioned left by coercive single-layer operators, (2) their unknowns physical quantities, i.e.,...

We present a new class of well-conditioned integral equations for the solution two and three dimensional scattering problems by homogeneous penetrable scatterers. Our novel boundary result from using regularizing operators which are suitable approximations admittance that map transmission conditions to exterior and, respectively, interior Cauchy data on interface between media. refer these regularized as generalized combined source (GCSIE). The can be expressed in terms Dirichlet-to-Neumann...

This work, part I in a two-part series, presents: (i) simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well (ii) an associated boundary-integral equation method the numerical solution problems scattering waves by doubly periodic arrays scatterers three-dimensional space. Except certain ‘Wood frequencies’ at which function ceases to exist, proposed approach, is based on smooth windowing gives rise tapered lattice sums converge superalgebraically fast...

We present a comparison among the performance of solvers based on Nystr\"om discretizations several well-posed boundary integral equation formulations Helmholtz transmission problems in two-dimensional Lipschitz domains. Specifically, we focus following four classes problems: (1)~the classical first kind equations for problems~\cite {costabel-stephan}, (2)~the second {KressRoach}, (3)~the single formulations~\cite {KleinmanMartin}, and (4)~certain direct counterparts recently introduced...

This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly hypersingular, and nearly singular integral kernels present in 3D Helmholtz surface layer potentials associated operators. Relying on Green's third identity pointwise functions form planewaves, these allow operators to be expressed terms integrand that remain bounded or even more regular regardless location target point relative sources. Common challenging integrals arise both...

Journal Article High-order Nyström discretizations for the solution of integral equation formulations two-dimensional Helmholtz transmission problems Get access Yassine Boubendir, Boubendir Department Mathematical Sciences and Center Applied Mathematics, NJIT, Univ. Heights. 323 Dr. M.L. King Jr. Blvd, Newark, NJ 07102, USAboubendi@njit.educatalin.c.turc@njit.edu Search other works by this author on: Oxford Academic Google Scholar Catalin Turc, Turc Víctor Domínguez * Departamento de...

Abstract Helmholtz decompositions of elastic fields is a common approach for the solution Navier scattering problems. Used in context boundary integral equations (BIE), this affords solutions problems via simpler operators (BIOs). Approximations Dirichlet-to-Neumann (DtN) can be employed within regularizing combined field strategy to deliver BIE formulations second kind two dimensions with Dirichlet conditions, at least case smooth boundaries. Unlike and transmission problems, approximations...

This work presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near "Wood anomaly frequencies". At these frequencies, one more grazing Rayleigh waves exist, and the lattice sum quasi-periodic Green function ceases to exist. We present a modification this adding two types terms it. The first type adds linear combinations "shifted" functions, ensuring that spatial singularities introduced are located below grating therefore outside...

We present a Schur complement domain decomposition (DD) algorithm for the solution of frequency multiple scattering problems. Just as in classical DD methods, we (1) enclose ensemble scatterers bounded by an artificial boundary, (2) subdivide this into collection non-overlapping subdomains so that boundaries do not intersect any and (3) connect solutions subproblems via Robin boundary conditions matching on common interfaces between subdomains. use subdomain Robin-to-Robin maps to recast...

We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helm\-holtz equations with impedance conditions in two-dimensional Lipschitz domains. consider both the case classical conditions, as well transmission wherein impedances are certain coercive operators. The latter type problem is instrumental speed up convergence Domain Decomposition Methods for Helmholtz problems. Our regularized use unknowns Dirichlet traces solution on domain....

We present a new high-order numerical method for the solution of high-frequency scattering problems from rough surfaces in three dimensions. The is based on asymptotic appropriate integral equations regime, manner that bypasses need to resolve fields scale wavelength radiation. Indeed, inspired by prior work two dimensions, we seek equation form slow modulation incoming radiation, and choose series expansion inverse powers wavenumber represent unknown slowly varying envelope. As show, this...