An iterative filter for solution of the inverse heat-conduction problem

An iterative modification of the nonlinear Kalman filter is proposed for the determination of time-variable heat-transfer coefficients.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 916–923, November, 1978.     

Approximation of the solution of inverse problem of scattering of electromagnetic waves on plane dielectrics

We propose a method for the determination of the material parameters of dielectric coatings according to the measured values of scattered electromagnetic fields which enables us to introduce an efficient procedure of processing of the data of measurements in the methods of nondestructive testing. As a specific feature of the proposed method for the solution of the formulated inverse problem, we can mention the possibility of reconstruction of piecewise continuous profiles of dielectric permittivity for laminated materials. The procedure of reconstruction is based on the method of integral equations. The solution of the problem is obtained approximately. The measured values of the coefficient of reflection of plane electromagnetic waves are extrapolated to the high-frequency region, which enables us to guarantee higher accuracy of reconstruction of the functions of dielectric permittivity for the analyzed structures.     

Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem

This paper investigates the signal-subspace method approach to solve the electromagnetic inverse scattering problem using intensity-only (phase-free) data. Due to the polarization of electromagnetic fields, the relationship between the rank of the multistatic matrix and the number of small scatterers is different from that associated with the scalar wave. Multiple scattering between scatterers is considered, and the inverse scattering problem of determining the polarization tensors is nonlinear, which, however, is solved by the proposed analytical approach where no associated forward problem is iteratively evaluated.     

Finite element solution for electromagnetic scattering from two-dimensional bodies

The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non-physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.     

Iterative solution of inverse scattering for a two-dimensional dielectric object

Two-dimensional inverse scattering for a dielectric cylinder was investigated. The problem was to reconstruct the dielectric constant distribution of a scatterer from the scattered field measured outside under the illumination of an incident wave. Theoretically, the inversion algorithm is derived using integral equation formulations together with the iterative technique. Note that the inverse problem is solved in the angular spectral domain instead of in the space domain. Therefore, the ill-posedness can be reduced and no regularization is needed. Numerical results show that with only one incident wave generated by a line source, good reconstruction is obtained even when the dielectric constant is fairly large and the Born approximation is no longer valid. The effects of random noise and measurement distance on imaging reconstruction were also investigated. © 1996 John Wiley & Sons, Inc.     

Numerical solution to a two-dimensional inverse heat conduction problem

The two-dimensional inverse heat conduction problem is solved using the method of dynamic programming. One problem involves determining two unknown heat flux histories imposed on two faces of a slab. Several numerical experiments were performed to ascertain the effects of noise and the weighting parameters.     

An overdeterrnined two-dimensional transient inverse heat conduction problem

The method of solving the two-dimensional nonlinear inverse heat conduction problems is presented. The time- and space temperature distribution inside a solid and heat transfer coefficient distribution on the boundary of the solid is determined based on the temperature histories measured in several selected inside locations. The problem is overdetermined because the number of measuring points is higher than the number of calculated parameters (components of heat transfer coefficient).     

Comparison of the born iterative method and tarantola's method for an electromagnetic time-domain inverse problem

Two methods of solving the nonlinear two-dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born-type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers.     

An iterative method for an inverse source problem of time-fractional diffusion equation

We propose an iteration method to recover a space-dependent source for a time-fractional diffusion equation from the final measurement. Based on the conditional stability of the inverse problem, we prove the convergence of the iterative regularization method under the a priori parameter choice rule and the a posteriori parameter choice rule, respectively. Numerical examples in one dimension and two dimension are given to validate the effectiveness of the presented method.     

Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems

Within the framework of inverse scattering problems, the quantifying of the degree of nonlinearity of the problem at hand provides an interesting possibility for evaluating the validity range of the Born series and for quantifying the difficulty of both forward and inverse problems. With reference to the two-dimensional scalar problem, new tools are proposed that allow the determination of the degree of nonlinearity in scattering problems when the maximum value, dimensions, and spatial-frequency content of the unknown permittivity are changed at the same time. As such, the proposed tools make it possible to identify useful guidelines for the solution of both forward and inverse problems and suggest an effective solution procedure for the latter. Numerical examples are reported to confirm the usefulness of the tools introduced and of the procedure proposed.     

Numerical solution of the inverse problem in the analysis of neutron small angle scattering experiments

A simple numerical procedure is presented to face particular problems encountered in the data analysis of small angle scattering studies of precipitation in complicated alloys. A suitable method for solving a least-squares problem with inequality constraints is suggested.     

An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. The iterative local search along with a shift strategy is developed and applied to the heuristic to balance the exploitation and exploration tasks in the solution space without the tuning of any parameters. The experimental results on many scales of packing problems show that this approach can produce high-quality solutions for most of the benchmark datasets, especially for large-scale problems, within a reasonable duration of computational time.     

Second-order iterative approach to inverse scattering: numerical results

We introduce an iterative algorithm for the reconstruction of dielectric profile functions from scattered field data, in which each step corresponds to the solution of a quadratic inversion problem. This means that, at each iteration, we perform a second-order approximation of the scattering operator connecting the unknown profile to the data about a reference profile function. This procedure is then compared with a linear iterative inversion algorithm, and it is pointed out that, within a prescribed class of profile functions, the linear iterative inversion does not converge to the actual solution, whereas the proposed approach does. This feature can be explained by reference not only to the improved approximation provided by the addition of a further term for profile functions of a larger norm but also to the different classes of functions that can be reconstructed by either the linear or the quadratic model. Numerical examples of profile reconstruction in the scalar two-dimensional geometry, with far-zone scattered field data at a fixed frequency, confirm the theoretical analysis.     

Analytic solution of the unsteady inverse heat-conduction problem

An algorithm is given for an approximate analytic solution of the unsteady inverse heat-conduetion problem for infinite and semi-infinite objects. The solution found in this manner is used to solve a special inverse problem of free diffusion.     

Application of iterative regularization for the solution of incorrect inverse problems

The solution of inverse heat-conduction problems using regularizing gradient algorithms is considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 5, pp. 843–851, November, 1987.     

Method of determining the thermophysical properties of orthotropic materials from the solution of a two-dimensional inverse heat-conduction problem

An unsteady two-dimensional inverse coefficient problem of heat conduction is formulated mathematically and solved.Translated from Inzhenefno-Fizicheskii Zhurnal, Vol. 56, No. 3, pp. 483–491, March, 1989.     

An iteration algorithm for the solution of the inverse boundary-value problem of heat conduction

An iterative procedure is constructed for solving the inverse boundary-value problem of heat conductivity in an extremal formulation on the basis of solving a Cauchy problem.     

A solution to the two-dimensional findpath problem

The 'findpath problem' a well-known problem in robotics, is the problem of finding a path for a moving solid among other solid obstacles. In this paper, a solution is proposed for the two-dimensional case where two point masses are required to move to designated areas or targets located in the horizontal plane while avoiding moving or stationary planar objects. The main tool used to solve the problem is the 'second or direct method of Liapunov', a powerful mathematical tool usually associated with the stability analysis of nonlinear systems. The theory developed from solving the two-dimensional findpath problem is then applied to the problem of cooperation between two planar robot arms. Computer simulations show the effectiveness of the proposed method     

An iterative regularization method for inverse phonon radiative transport problem in nanoscale thin films

An inverse phonon radiative transport problem with an alternative form of adjoint equation is solved in this study by using conjugate gradient method (CGM) to estimate the unknown boundary temperature distributions, based on the phonon intensity measurements. The CGM in dealing with the present integro‐differential governing equations is not as straightforward as for the normal differential equations; special treatments are needed to overcome the difficulties. Results obtained in this inverse analysis will be justified based on the numerical experiments where two different unknown temperature (or phonon intensity) distributions are to be determined. Finally, it is shown that accurate boundary temperatures can always be obtained with CGM. Copyright © 2006 John Wiley & Sons, Ltd.