microwave image reconstruction utilizing log magnitude and unwrapped phase to improve high contrast object recovery reconstructing images of large high contrast objects with microwave methods has proved difficult successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution in these situations the measured electric field phases as a function of receiver position around the periphery of the imaging field of view vary rapidly often undergoing changes of greater than spl pi radians especially when the object contrast and illumination frequency increase here the authors introduce a modified form of a maxwell equation model based image reconstruction algorithm which directly incorporates log magnitude and phase of the measured electric field data by doing so measured phase variation can be unwrapped and distributed over more than one rieman sheet in the complex plane simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high contrast objects simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures of merit which estimate when it is critical to deploy the new image reconstruction approach in these cases the new algorithm recovers high quality images without resorting to the use of a priori information on object contrast and or size as previously required

singular value analysis of the jacobian matrix in microwave image reconstruction for non linear inverse scattering problems utilizing gauss newton methods the jacobian matrix encodes rich information concerning the system performance and algorithm efficiency in this paper we perform an analytical evaluation of a single iteration jacobian matrix based on a previously derived nodal adjoint representation concepts for studying linear ill posed problems such as the degree of ill posedness are used to assess the impact of important system parameters on the expected image quality analytical singular value decomposition svd of the jacobian matrix for a circular imaging domain is derived along with the numerical svd for optimizing imaging system configurations the results show significant reductions in the degree of ill posedness when signal frequency antenna array density and property parameter sampling are increased specifically the decay rate in the singular spectrum of the jacobian decreases monotonically with signal frequency being approximately 1 3 of its 0 1 ghz value at 3 ghz is improved with antenna array density up to about 35 equally spaced circumferentially positioned elements and drops significantly with increased property parameter sampling to more than twice the amount of measurement data these results should serve as useful guidelines in the development of design specifications for an optimized hardware installation

a block qmr method for computing multiple simultaneous solutions to complex symmetric systems the solution of complex symmetric indefinite systems of equations where multiple solutions are required is considered the quasi minimum residual qmr method ideally suited for these matrices is generalized using the block lanczos algorithm to solve multiple solutions simultaneously this modification alone is shown through numerical examples involving large sparse matrices from finite element discretization of maxwell s equations to accelerate the convergence by a factor almost as great as the number of simultaneous solutions a natural convergence criterion for this method is presented that is shown to be as effective as and easier to compute than the usual equation residual finally a numerical comparison of the classical incomplete cholesky and a variant of the ilu t preconditioners is given showing superior performance by the latter

viable three dimensional medical microwave tomography theory and numerical experiments three dimensional microwave tomography represents a potentially very important advance over 2d techniques because it eliminates associated approximations which may lead to more accurate images however with the significant increase in problem size computational efficiency is critical to making 3d microwave imaging viable in practice in this paper we present two 3d image reconstruction methods utilizing 3d scalar and vector field modeling strategies respectively finite element fe and finite difference time domain fdtd algorithms are used to model the electromagnetic field interactions in human tissue in 3d image reconstruction techniques previously developed for the 2d problem such as the dual mesh scheme iterative block solver and adjoint jacobian method are extended directly to 3d reconstructions speed improvements achieved by setting an initial field distribution and utilizing an alternating direction implicit adi fdtd are explored for 3d vector field modeling the proposed algorithms are tested with simulated data and correctly recovered the position size and electrical properties of the target the adjoint formulation and the fdtd method utilizing initial field estimates are found to be significantly more effective in reducing the computation time finally these results also demonstrate that cross plane measurements are critical for reconstructing 3d profiles of the target

two parallel symmetry permeable cracks in functionally graded piezoelectric piezomagnetic materials under anti plane shear loading abstract in this paper the behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric piezomagnetic materials subjected to an anti plane shear loading is investigated to make the analysis tractable it is assumed that the material properties c44 e15 e11 q15 d11 and 11 vary exponentially with coordinate parallel to the crack by using the fourier transform the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces these equations are solved using the schmidt method the normalized stress the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions numerical examples are provided to show the effect of the geometry of the interacting crack and the parameter describing the functionally graded materials upon the stress intensity factor of the cracks

property of positive solutions and its applications for sturm liouville singular boundary value problems abstract this paper is concerned with the property of the positive solutions for sturm liouville singular boundary value problems with the linear conditions we obtain a relation between the solutions and green s function it implies a necessary condition for the c 1 0 1 positive solutions we apply the result to conclude that the given equation has no c 1 0 1 positive solutions

the existence of countably many positive solutions for one dimensional p laplacian with infinitely many singularities on the half line we study the existence of countably many positive solutions of boundary value problems on the half line for differential equations of second order the fixed point index theory and a new fixed point theorem in cones are used

singular k n k boundary value problems between conjugate and right focal abstract for 1 k n 1 and 0 q k 1 solutions are obtained for the boundary value problem 1 n k f x y y i 0 0 i k 1 and y i 0 q j n k q 1 where f x y is singular at y 0 an application is made of a fixed point theorem for operators that are decreasing with respect to a cone

three dimensional green s functions in anisotropic piezoelectric solids abstract explicit expressions for three dimensional extended green s displacements in general anisotropic piezoelectric solids are derived a very efficient procedure for the numerical evaluation of the derivatives of the extended green s displacements is also proposed numerical comparisons are carried out for a transversely isotropic piezoelectric solid for which exact closed form solutions are available it is found that the extended green s displacements and their derivatives obtained with the present explicit formulation are in perfect agreement with the exact closed form solutions these green s functions can be used in the boundary integral equations for piezoelectric solids of general anisotropy and for subsequent numerical solutions of these equations by means of the boundary element method

stress intensity factors of a rectangular crack meeting a bimaterial interface using the hypersingular integral equation method based on body force method a planar crack meeting the interface in a three dimensional dissimilar materials is analyzed the singularity of the singular stress field around the crack front terminating at the interface is analyzed by the main part analytical method of hypersingular integral equations then the numerical method of the hypersingular integral equation for a rectangular crack subjected to normal load is proposed by the body force method which the crack opening dislocation is approximated by the product of basic density functions and polynomials numerical solutions of the stress intensity factors of some examples are given

inverse scattering an iterative numerical method for electromagnetic imaging the authors propose a spatial iterative algorithm for electromagnetic imaging based on a newton kantorovich procedure for the reconstruction of the complex permittivity of inhomogeneous lossy dielectric objects with arbitrary shape starting from integral representation of the electric field and using the moment method this technique has been developed for 2 d for tm and te polarization cases objects as well as for 3 d objects its performance has been compared with spectral techniques of classical diffraction tomography the modified newton method and the pseudo inverse method

microwave image reconstruction from 3 d fields coupled to 2 d parameter estimation an efficient gauss newton iterative imaging technique utilizing a three dimensional 3 d field solution coupled to a two dimensional 2 d parameter estimation scheme 3 d 2 d is presented for microwave tomographic imaging in medical applications while electromagnetic wave propagation is described fully by a 3 d vector field a 3 d scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy in addition the image recovery has been restricted to 2 d but is generalizable to three dimensions image artifacts related primarily to 3 d effects are reduced when compared with results from an entirely two dimensional inversion 2 d 2 d important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for jacobian construction methods which enhance the image quality such as the log magnitude unwrapped phase minimization were also applied results obtained from synthetic measurement data show that the new 3 d 2 d algorithm consistently outperforms its 2 d 2 d counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts

integral identities based on symmetric and skew symmetric weight functions for a semi infinite interfacial crack in anisotropic magnetoelectroelastic bimaterials abstract in this paper we address a semi infinite interfacial crack problem in an anisotropic magnetoelectroelastic mee bimaterial system subjected to a magnetoelectromechanical asymmetric load on the crack surface first the symmetric and skew symmetric weight functions are derived for a two dimensional 2 d deformation problem using these weight functions and extending the betti formula to mee materials the integral identities are further obtained and the present crack problem is formulated in terms of singular integral equations which establish the relationship between the applied external load and the generalized displacement jump across the crack faces the illustrative examples in relation to mode iii and mode i and mode ii problems show that the method developed in this study avoids the use of green s function and is very convenient for the fracture analysis of mee solids in which a multi field coupled effect is observed

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

stochastic optimization methods applied to microwave imaging a review stochastic methods are now very common in electromagnetics among the various applications they have been recently proposed for solving inverse problems arising in radio frequency and microwave imaging some of the recently proposed stochastic inversion procedures are critically discussed e g genetic algorithms differential evolution methods memetic algorithms particle swarm optimizations hybrid techniques etc and the way they have been applied in this area the use of the ant colony optimization method which is a relatively new method in electromagnetics is also proposed various imaging modalities are considered tomography buried object detection and borehole sensing finally the main features making these approaches useful for imaging purposes are discussed and the currently considered strategies to reduce the computational load associated with stochastic optimization procedures delineated

positive solutions of nonresonance semipositone singular dirichlet boundary value problems abstract in the case where the nonlinearity term is allowed to change sign we study the nonresonance semipositone singular dirichlet boundary value problem bvp x p t x f t x g t x 0 t 1 x 0 x 1 0 where 0 is a parameter 0 is a constant we derive an interval of such that for any lying in this interval the semipositone bvp has at least one positive solution if f is superlinear or sublinear the results obtained improve and extend many recent results our approach is based on krasnaselskii s fixed point theorem in cones

positive solutions of semi positone hammerstein integral equations and applications abstract existence of solutions for semi positone integral equations of hammerstein type is obtained by using the fixed point index method many boundary value problems of differential equations can be transformed into these integral equations a specific example is given

the existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the p laplacian operator abstract in this paper we study the existence of countable many positive solutions for a class of nonlinear singular boundary value systems with p laplacian operator p 1 u a 1 t f u v 0 0 t 1 p 2 v a 2 t g u v 0 0 t 1 1 p 1 u 0 1 p 1 u 0 0 1 p 1 u 1 1 p 1 u 1 0 2 p 2 v 0 2 p 2 v 0 0 2 p 2 v 1 2 p 2 v 1 0 where p i s s p i 2 s p i 1 f g are lower semi continuous functions a i t has countable many singularities on 0 1 2 i 1 2 by using the fixed point theorem of cone expansion and compression of norm type the existence of countable many positive solutions for nonlinear singular boundary value system with p laplacian operator are obtained

on multiple circular inclusions in plane magnetoelasticity abstract a general series solution to the magnetoelastic problem of interacting circular inclusions in plane magnetoelasticity is provided in this paper by the use of complex variable theory and laurent series expansion method the general expression of the magnetic and the magnetoelastic complex potentials for the circular inclusion problem is derived expanding the definition of the airy s stress function of pure elastic field into the magnetoelastic field and applying the superposition method the general expression then can be reduced to a set of linear algebraic equations and solved in a series form an approximate closed form solution for the case of two arbitrarily located inclusions is also provided for illustrating the effect of the pertinent parameters the numerical results of the interfacial magnetoelastic stresses are displayed in graphic form

magneto thermo electro elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings abstract the article presents an analytical solution for magneto thermo electro elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock mechanical load and transient electric excitation using an interpolation method solves the volterra integral equation of the second kind caused by interaction among magnetic thermal electric and mechanical fields the electric displacement is determined thus the exact expressions for the transient responses of displacement stresses electric displacement electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of hankel transforms laplace transforms and inverse laplace transforms from sample numerical calculations it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock mechanical load and transient electric excitation and the result carried out may be used as a reference to solve other transient coupled problems of magneto thermo electro elasticity

the existence of positive solutions for a nonlinear four point singular boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for the nonlinear four point singular boundary value problem with a p laplacian operator by using the fixed point index theory the existence of a positive solution and many positive solutions for a nonlinear four point singular boundary value problem with a p laplacian operator are obtained

the magnetoelastic problem of cracks in bonded dissimilar materials abstract in this paper we consider the magnetoelastic problem of straight cracks lying along interface of two dissimilar soft ferromagnetic materials subjected to remote uniform magnetic induction based on the hilbert problem formulation and the technique of analytical continuation closed form solution for magnetic fields and both the magnetoelastic stresses and the maxwell stresses are obtained it is found that the singularity of magnetoelastic stresses has similar trig log character as those obtained for pure elastic problems which were free from the discontinuous jumps of the magnetic properties and fields across the interface for illustrating the use of present approach the detailed results for a single crack case are provided and verified by comparison with the existing ones under special cases the numerical examples of magnetoelastic stress distribution for different material properties are presented graphically expressions of the stress intensity factors in the vicinity of crack tip and crack opening condition are also derived it is shown that the crack open assumption is valid except a limiting range of distance measured from the crack tip

application of hypersingular integral equation method to three dimensional crack in electromagnetothermoelastic multiphase composites a three dimensional crack problem in electromagnetothermoelastic multiphase composites emte mcs under extended loads is investigated in this paper using green s functions the extended general displacement solutions are obtained by the boundary element method this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations in which the unknown functions are the extended displacement discontinuities then the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main part analysis method of hypersingular integral equations analytical solutions for the extended singular stresses the extended stress intensity factors sifs and the extended energy release rate near the crack front in emte mcs are provided also a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials in addition distributions of extended sifs varying with the shape of the crack are presented the results show that the present method accurately yields smooth variations of extended sifs along the crack front

analysis of 3d fluid driven crack propagation problem in co seismic slip under p and s waves by hybrid hypersingular integral method this work reports a new and accurate way of theoretical and numerical description of the extended 3d fluid electromagnetic and flow driven crack progression in co seismic slip under p and s waves first based on the viscous fluid flow reciprocal work theorem the hybrid hypersingular integral equation hie method proposed by the author was defined by combined with the coupled extended wave time domain hie and the extended diffused interface phase field method the general extended 3d fluid flow velocity wave solutions are obtained by the extended wave time domains green s function method the 3d extended dynamic fluid driven crack modeling under fully coupled electromagnetothermoelastic p and s wave and flow field was established then the problem is reduced to solving a set of extended hybrid hies coupled with nonlinear boundary domain integral equations in which the unknown functions are the general extended flow velocity discontinuity waves the behavior of the general extended singular stress indices around the crack front terminating is analyzed by hybrid time domain main part analysis the general extended singular pore stress waves spsws and the extended dynamic stress intensity factors dsifs on the fluid driven crack surface are obtained from closed form solutions in addition a numerical method for the problem is proposed in which the extended velocity discontinuity waves are approximated by the product of time domain density functions and polynomials the extended dsifs and general extended spsws are calculated and the results are presented toward demonstrating the applicability of the proposed method

spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumor a reconstruction algorithm to simultaneously estimate the shape and location of three dimensional breast cancer tumor is presented and its utility is analyzed the approach is based on a spherical harmonic decomposition to capture the shape of the tumor we combine a gradient descent optimization method with a direct electromagnetic solver to determine the coefficients in the harmonic expansion as well as the coordinates of the center of the tumor the results demonstrate the potential advantage of collecting data using a multiple view tomographic type strategy we show how the order of the harmonic expansion must be increased to capture increasingly irregularly shaped tumors and explore the resulting increase in the central processing unit cpu time required by the algorithm our approach shows accurate reconstruction of the tumor image regardless of the source polarization this work demonstrates the promise of the algorithm when used on data corrupted with gaussian noise and when perfect knowledge of the tumor electrical properties is not available

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

enhancement of the krylov subspace regularization for microwave biomedical imaging although krylov subspace methods provide fast regularization techniques for the microwave imaging problem they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction to suppress these spurious oscillations and to provide an edge preserving regularization we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm we show the inversion results for a real human forearm assuming the 2 d transverse magnetic illumination and a cylindrical object assuming the 2 d transverse electric illumination

fracture analysis in continuously nonhomogeneous magneto electro elastic solids under a thermal load by the mlpg abstract a meshless method based on the local petrov galerkin approach is proposed to solve initial boundary value problems of magneto electro elastic solids with continuously varying material properties stationary and transient thermal problems are considered in this paper the mechanical 2 d fields are described by the equations of motion with an inertial term nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity the spatial variation of displacements electric and magnetic potentials is approximated by the moving least squares mls scheme after performing the spatial integrations one obtains a system of ordinary differential equations for certain nodal unknowns that system is solved numerically by the houbolt finite difference scheme as a time stepping method

the existence of countably many positive solutions for nonlinear singular m point boundary value problems in this paper we study the existence of countably many positive solutions for nonlinear singular boundary value problem f u a t f u t 0 0r is an increasing homeomorphism and positive homomorphism and f 0 0 x i 0 1 with 0 0 and has countably many singularities in 0 12 we show that there exist countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

a multiplicity result for a boundary value problem with infinitely many singularities abstract we consider the second order boundary value problem u t a t f u t 0 where a t lp 0 1 for some p 1 and has countably many singularities in 0 1 2 we show that there exist countably many positive solutions using holder s inequality and krasnosel skii s fixed point theorem for operators on a cone