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An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a time-dependent transmission problem for a thermo-electric-magneto-elastic solid immersed in an inviscid and compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided an appropriate scaling factor is employed. Based on estimates of variational solutions in the Laplace-transformed domain, we obtain the properties of corresponding solutions in the time-domain without having to perform explicit inversions of the variational solutions in the Laplace-transformed domain. [ABSTRACT FROM AUTHOR]

We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's approach, through a passage to the Laplace domain. We focus on the cases where one of the unknown fields satisfies a Dirichlet boundary condition, while the other one is subject to conditions of Neumann type. In the Laplace domain, combined simple-and double-layer potential boundary integral operators are introduced and proven to be coercive. Based on the Laplace domain estimates, it is possible to prove the existence and uniqueness of solutions in the time domain. This analysis complements previous results that may serve as the mathematical foundation for discretization schemes based on the combined use of the boundary element method and convolution quadrature. [ABSTRACT FROM AUTHOR]

This paper is concerned with the application of time-domain boundary integral methods to a nonstationary boundary value problem for the thermo-elasto-dynamic equations, based on the Lubich approach via the Laplace transform. Fundamental solutions of the transformed thermo-elasto-dynamic equations are constructed explicitly by the Hörmander method. Simpleand double-layer potential boundary integral operators are introduced in the transformed domain, and their coercivity is established. Based on the estimates of various boundary integral operators in the transformed domain, existence and uniqueness results of solutions are established in the time domain. These results may serve as a mathematical foundation for the semidiscretization and full-discretization schemes based on the boundary element method and the convolution quadrature method for time domain boundary integral equations arising in thermoelasticity [ABSTRACT FROM AUTHOR]

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a generalization of the coupling procedure employed by the authors for the treatment of the time-dependent fluid–structure interaction problem. Using an integral representation of the solution in the infinite exterior domain occupied by the fluid, the problem is reduced to one defined only over the finite region occupied by the solid, with nonlocal boundary conditions. The nonlocal boundary problem is analysed with Lubich's approach for time-dependent boundary integral equations. Existence and uniqueness results are established in terms of time-domain data with the aid of Laplace domain techniques. Galerkin semidiscretization approximations are derived and error estimates are obtained. A full discretization based on the convolution quadrature method is also outlined. Some numerical experiments in two dimensions are also included in order to demonstrate the accuracy and efficiency of the procedure. [ABSTRACT FROM AUTHOR]

This paper is concerned with boundary integral equation methods for solving the two-dimensional uid-solid interaction problem. We reduce the problem to three different systems of boundary integral equations via direct and indirect approaches. Existence and uniqueness results for variational solutions of boundary integral equations are established. Since in all these variational formulations, the hypersingular boundary integral operator associated with the time-harmonic Navier equation is a dominating integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a weakly singular kernel. Numerical examples are presented to verify and validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three different systems of boundary integral equations via direct and indirect approach es. Existence and uniqueness results for variational solutions of boundary integral equations are established. Since in all these variational formulations, the hypersingular boundary integral operator assoc iated with the time-harmonic Navier equation is a dominating integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a weakly singular kernel. Numerical examples are presented to verify and validate the theoretical results. [ABSTRACT FROM AUTHOR]

We prove an existence theorem for the anisotropic, time-harmonic poro-elastic boundary value problem by using the Gårding inequality. [ABSTRACT FROM AUTHOR]

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of the central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical fluid-structure interaction problem by using a coupling procedure that reduces the problem to a nonlocal initial-boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time-dependent fluid-structure interaction problems by convolution quadrature coupling of FEM and BEM. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well-posedness along with stability and error bounds with explicit time dependence are established. Full discretization is achieved coupling boundary and finite elements; convolution quadrature (CQ) is used for time evolution in the pure boundary integral equation formulation and combined with time stepping in the coupled boundary-finite element method (BEM-FEM) scenario. Second-order convergence in time is proved for BDF2-CQ and numerical experiments are provided for both BDF2 and trapezoidal rule CQ showing second-order behaviour for the latter as well. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary integral representation, using Galerkin semidiscretization in the space variables and multistep convolution quadrature in time. Convergence estimates are based on a Laplace domain analysis, which translates into a detailed study of the exterior Brinkman problem. Some numerical experiments are provided [ABSTRACT FROM AUTHOR]

We reduce an exterior initial boundary value problem for the wave equation in three space dimensions to an initial boundary value problem on a bounded computational domain bounded by an artificial boundary as well as the original boundary. From a Kirchhoff representation formula for the solution of wave equation in an exterior domain, we derive on the artificial boundary (exact) transparent boundary conditions that are nonlocal in space and time. These lead to local approximate transparent boundary conditions of the first and second orders. It is shown that these approximate transparent conditions are satisfied exactly for a related spherically symmetric problem. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & Nédélec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the wellknown Babuška-Brezzi theory: in particular, the well-posedness of the formulation will be established. [ABSTRACT FROM AUTHOR]

We give an elementary, rigorous and self-contained derivation of a Kirchhoff representation formula for solutions of the wave equation for a bounded region in three-dimensional space for the case of non-homogeneous initial conditions. A special feature of the result is the role of spherical caps which seems not to be noticed previously. The formula is readymade for boundary integral formulations of initial/boundary-value problems for the wave operator. [ABSTRACT FROM AUTHOR]

In this article, a variational formulation for the transmission problem of the fluid-bone interaction is formulated. The formulation is based on a modified Biot system of equations for the cancellous bone together with a boundary integral equation formulation of the pressure in the water. Existence and uniqueness for the weak solution of the interaction problem are established in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]

We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The inverse problem of determining the shape of such an elastic scatterer from the measured far field pattern of the scattered fluid pressure field is of central importance in detecting and identifying submerged objects. Following a method proposed by Kirsch and Kress, we approximate the acoustic and elastodynamic wave by potentials over auxiliary surfaces, and we reformulate the inverse problem as an optimization problem. The objective function to be minimized is the sum of three terms. The first is the deviation of the approximate far field pattern from the measured one, the second is a regularization term, and the last a control term for the transmission condition. We prove that the optimization problem has a solution and that, for the regularization parameter tending to zero, the minimizers tend to a solution of the inverse problem. In contrast to a numerical method from a previous paper, the presented method requires neither a direct solution method nor an additional treatment of possible Jones modes. [ABSTRACT FROM AUTHOR]

In this article we offer a novel method for interrogating cancellous bone using ultra sound measurements. The problem is first modelled in terms of the acoustic pressure in the water bath surrounding the bone sample, the pore pressure and the displacement of the elastic matrix describing the cancellous bone specimen. The fluid pressure in the water tank is represented in terms of a boundary integral equation. Source points are placed on a parallel line on one side of the bone; whereas, receivers are placed on the other side of the bone. Sensitivity tests are run for two frequencies which show that the corresponding inverse problem leads to reasonable good results. [ABSTRACT FROM AUTHOR]

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions. [ABSTRACT FROM AUTHOR]

This article is concerned with the application of the Newton-imbedding iteration procedure to nonlinear boundary value problems in Sobolev spaces. A simple model problem for the second-order semilinear elliptic equations is considered to illustrate the main idea. The essence of this method hinges on the a priori estimates of solutions of the associated linear problem in appropriate Sobolev spaces. It is to our surprise that H 1 (Ω)-solution is not smooth enough to guarantee the convergence of the sequence generated by the procedure. Existence and uniqueness of solution to the original nonlinear problem are established constructively. An application of this approach to the Lamé system with nonlinear body force and its generalization to contain a nonlinear surface traction in elasticity is also discussed. [ABSTRACT FROM AUTHOR]

This article is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green's formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different parts of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]

In recent years, inverse scattering problems have received much attention because of their important applications. Given the incident and scattered waves, an inverse scattering problem in general is to determine the properties of the scatterer. In radar or sonar a known incident wave and observed scattered wave are used to detect the properties and the presence of aircraft or submarine objects; in MRI scanning, tomography X-rays and ultrasound, scattered waves are used to determine the presence or properties of tumors by detecting density variations, to name a few. In this article, we are concerned with the two-dimensional electromagnetic inverse scattering problem. An iterative algorithm for the transversal electric waves will be given based on a singular domain integral equation formulation. Basic features of a scattering object such as shape, location and index of refraction will be recovered from measurements of the field scattered by the object (when illuminated by electromagnetic waves with the magnetic vector polarized along the cylinder axis). Some numerical experiments are included to illustrate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In a previous paper the authors studied transient elastic wave propagation in woven fabric composites under impact loading. A one-dimensional analysis was developed to predict the elastodynamic and elastostatic behavior. The initial and boundary value problem was formulated and then solved using Laplace transforms. In this paper we examine the same problem using an alternative approach based upon the combination of Laplace transforms and finite Fourier transforms. Using this approach, some of the difficulties caused by the inversion of Laplace transforms encountered in the previous work are overcome. Analytical solutions to dynamic displacements and stresses, including bond shearing stresses, can be obtained for any type of impact loading. The merits as well as the shortcomings of the alternative approach are discussed. It is found that for elastodynamic problems the solution given in this paper are better than those reported in the previous work, since there is no need to perform the numerical inversion of Laplace transforms before superposition of the solutions of the two component problems. On the other hand, for elastostatic problems the solutions given in the previous work are more concise. [ABSTRACT FROM PUBLISHER]

Addresses the problem of estimation in the numerical solution of integral equations that arise in electromagnetics. Integral representations; Irregular frequencies; Calderon projectors; Finite energy and function spaces; Mapping properties; Residual errors; The perfectly conducting sphere; Conclusions.

A theoretical analysis has been performed to evaluate the dynamic stress concentration factor in hybrid composites composed of low elongation (LE) and high elongation (HE) fibers. At a fracture of a fiber, the present model predicts two stress waves propagating along each fiber in the hybrid. The phase difference of the dynamic responses contributed by these waves at the middle section of a fiber immediately adjacent to a fiber breakage is controll ed by the fiber mass per unit length. The magnitude of the dynamic responses is determined by the fiber extensional stiffness. The study concludes that hybrid effect always exists in a beneficial manner and the case of the parent LE fiber composite provides the upper bound for the dynamic stress concen tration factor in hybrids. The validity of the approximations made in the derivations has been examined. [ABSTRACT FROM PUBLISHER]

The convergence characteristics of h- and p- extensions of the finite element method in the case of singularly perturbed boundary value problems are presented. For this purpose, two model problems are considered: i) a reaction-diffusion problem with large Thiele modulus; and ii) a convection-diffusion problem with large Peclet number. Based on a large number of numerical studies, it is concluded that p-extension leads to superior performance due to significantly faster convergence rates coupled with convenience in modeling. [ABSTRACT FROM PUBLISHER]