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To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.

The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.

The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.

Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.

The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.

A method has been developed for the solution of inverse heat diffusion problems to find the initial condition, boundary condition, and the source and sink function in the heat diffusion equation. The method has been used in the development of a source‐and‐sink method to find the boundary conditions in inverse Stefan problems. Green's functions have been used in the solution, and the problems are solved by using two approaches: a series solution approach, and a time incremental approach. Both can be used to find the boundary conditions without reliance on the flux information to be supplied at both sides of the interface. The methods are efficient in that they require less equations to be solved for the conditions. The numerical results have shown to be accurate, convergent, and stable. Most of all, the results do not degrade with time as in other time marching schemes reported in the literature. Algorithms can also be easily developed for the solution of the conditions.

The purpose of this paper is to propose novel factored approximate sparse inverse schemes and multi-level methods for the solution of large sparse linear systems.

The main motive for the derivation of the various generic preconditioning schemes lies to the efficiency and effectiveness of factored preconditioning schemes in conjunction with Krylov subspace iterative methods as well as multi-level techniques for solving various model problems. Factored approximate inverses, namely, Generic Factored Approximate Sparse Inverse, require less fill-in and are computed faster due to the reduced number of nonzero elements. A modified column wise approach, namely, Modified Generic Factored Approximate Sparse Inverse, is also proposed to further enhance performance. The multi-level approximate inverse scheme, namely, Multi-level Algebraic Recursive Generic Approximate Inverse Solver, utilizes a multi-level hierarchy formed using Block Independent Set reordering scheme and an approximation of the Schur complement that results in the solution of reduced order linear systems thus enhancing performance and convergence behavior. Moreover, a theoretical estimate for the quality of the multi-level approximate inverse is also provided.

Application of the proposed schemes to various model problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than results by other researchers for some of the model problems.

Further enhancements are investigated for the proposed factored approximate inverse schemes as well as the multi-level techniques to improve quality of the schemes. Furthermore, the proposed schemes rely on the definition of multiple parameters that for some problems require thorough testing, thus adaptive techniques to define the values of the various parameters are currently under research. Moreover, parallel schemes will be investigated.

The proposed approximate inverse preconditioning schemes as well as multi-level schemes are efficient computational methods that are valuable for computer scientists and for scientists and engineers in engineering computations.

The purpose of this paper is to present a simple approach for calculation of the sensitivities in the free-form inverse design problems. The approach is based on the analogy with the similar tasks used in the signal-processing analysis. In the proposed case it is not required to solve an adjoint problem as in the most of the similar optimization tasks. The simulation engine used in the background is a Fast Boundary Element Method. The approach is validated on some known benchmark problems.

Inverse design is recognized nowadays as a crucial scientific grand challenge. Contrary to the conventional approach (“Given the structure, find the properties”) it purses a new paradigm (“Given the desired property, find the structure”). Inverse class of problems has a broad application area, from the material-, medical-, bio- to the engineering-class of problems. When dealing with the inverse design in free-form optimization of the engineering problems the typical approach is to calculate the adjoint problem. Calculation of the adjoint problem mostly requires the costly calculation of the gradients, which makes the whole optimization procedure rather expensive due to the high computational burden required for their solution.

In this paper it is proposed a novel Simple Sensitivity Approach to get in a fast way the response (sensitivity) function of the analyzed structure. The simulation engine used in the background is the Fast Boundary Element Method.

Novel approach for inverse design when performing the free-form optimization of engineering problems.

In the context of electrical impedance tomography (EIT), this paper aims to evaluate limitations of estimating conductivity or resistivity, as well as the improvements achieved with the use of an alternate description of the solution space, the logarithmic conductivity.

A quantitative analysis is performed, solving the inverse EIT problem by using the Gauss–Newton and non-linear conjugate gradient methods for a numerical phantom of 15 elements. A property of symmetry is studied for the direct EIT problem for a phantom of 385,601 elements.

Solving the inverse EIT problem in logarithmic conductivity is more robust to the initial guess, as solutions are kept within physical bounds (conductivity positiveness). Also, convergence is faster and less dependent on the final values of the estimates.

Logarithmic conductivity provides an advantageous description of the solution space for the EIT inverse problem. Similar estimation problems might be subject to analogous conclusions.

This study provides a novel analysis, quantitatively comparing the effect of different variables to solve the inverse EIT problem.

The purpose of this paper is to develop an inverse approach for 3D thermal sources determination.

The developed approach is based on the Green's function for Poison's equation. Forward and inverse couple electromagnetic‐thermal field problems are formulated. Finite elements models are built and applied. Thermal field data are acquired by thermo vision camera. The thermal field sources are determined inside of the investigated inaccessible volume object using modeled and measured data with the developed approach.

The presented method and implemented examples demonstrate the possibilities of the developed approach for inverse source problem solution and determination of thermal field distributions of electrical devices.

The proposed inverse method uses the Green's function for Poison's equation for solution of thermal field problem taking into account the couple electromagnetic‐thermal problems. Proposed inverse method is very fast, accurate and can be used in many practical activities for electrical current determination and visualization in inaccessible regions only by measured external thermal field. Thermal field data needed for the method are easily acquired by thermo vision camera.

Solves the inverse problem of estimating the wall heat flux in a parallel plate channel, by using the conjugate gradient method with adjoint equation. The unknown heat flux is supposed to vary in time and along the channel flow direction. Examines the accuracy of the present function estimation approach, by using transient simulated measurements of several sensors located inside the channel. The inverse problem is solved for different functional forms of the unknown wall heat flux, including those containing sharp corners and discontinuities, which are the most difficult to be recovered by an inverse analysis. Addresses the effects on the inverse problem solution of the number of sensors, as well as their locations.

The purpose of this paper is to develop a numerical model for estimating the unknown boundary heat flux in a parallel plate channel for the case of a hydrodynamically and thermally developing laminar flow.

The conjugate gradient method (CGM) is used to solve the inverse problem. The momentum equations are solved using an in-house computational fluid dynamics (CFD) source code. The energy equations along with the adjoint and sensitivity equations are solved using the finite volume method.

The effects of number of measurements, distribution of measurements and functional form of unknown flux on the accuracy of estimations are investigated in this work. The prediction of boundary flux by the present algorithm is found to be quite reasonable.

It is noticed from the literature review that study of inverse problem with hydrodynamically developing flow has not received sufficient attention despite its practical importance. In the present work, a hydrodynamically and thermally developing flow between two parallel plates is considered and unknown transient boundary heat flux at the upper plate of a parallel plate channel is estimated using CGM.

To reduce the heat load of a gas turbine blade, its surface is covered with an outer layer of ceramics with high thermal resistance. The purpose of this paper is the selection of ceramics with such a low heat conduction coefficient and thickness, so that the permissible metal temperature is not exceeded on the metal-ceramics interface due to the loss ofmechanical properties.

Therefore, for given temperature changes over time on the metal-ceramics interface, temperature changes over time on the inner side of the blade and the assumed initial temperature, the temperature change over time on the outer surface of the ceramics should be determined. The problem presented in this way is a Cauchy type problem. When analyzing the problem, it is taken into account that thermophysical properties of metal and ceramics may depend on temperature. Due to the thin layer of ceramics in relation to the wall thickness, the problem is considered in the area in the flat layer. Thus, a one-dimensional non-stationary heat flow is considered.

The range of stability of the Cauchy problem as a function of time step, thickness of ceramics and thermophysical properties of metal and ceramics are examined. The numerical computations also involved the influence of disturbances in the temperature on metal-ceramics interface on the solution to the inverse problem.

The computational model can be used to analyze the heat flow in gas turbine blades with thermal barrier.

A number of inverse problems of the type considered in the paper are presented in the literature. Inverse problems, especially those Cauchy-type, are ill-conditioned numerically, which means that a small change in the inputs may result in significant errors of the solution. In such a case, regularization of the inverse problem is needed. However, the Cauchy problem presented in the paper does not require regularization.

The purpose of the study is to solve numerically the inverse problem of determining the time-dependent convection coefficient and the free boundary, along with the temperature in the two-dimensional convection-diffusion equation with initial and boundary conditions supplemented by non-local integral observations. From the literature, there is already known that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data.

For the numerical discretization, this paper applies the alternating direction explicit finite-difference method along with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted.

The numerical results demonstrate that accurate and stable solutions are obtained.

The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical solution has been realized so far; hence, the main originality of this work is to attempt this task.