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Defect Identification in Electrical Circuits via the Virtual Distortion Method. Part 1: *Steady-state* *Case*

"... ABSTRACT: Virtual Distortion Method, a numerical technique originally developed and applied to various optimization problems in structural mechanics, is adapted to DC/AC circuit analysis. Electro-mechanical analogies with discrete models of plain truss structures are utilized to introduce and implem ..."

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ABSTRACT: Virtual Distortion Method, a numerical technique originally developed and applied to various optimization problems in structural mechanics, is adapted to DC/AC circuit analysis. Electro-mechanical analogies with discrete models of plain truss structures are utilized to introduce and implement the main concepts of the method. Simulation of conductance modifications in circuit elements by the equivalent set of virtual sources is a foundation of numerically effective algorithms enabling fast re-analysis and sensitivity analy-sis. Inverse problem of defect identification is discussed and solution based on distortion approach is provided. Key Words: optimization, embedded intelligence, structural health monitoring.

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control for the Hamilton-Jacobi equations. Part I: The one-dimensional *steady* *state* *case*

, 2004

"... In this paper, we introduce a new adaptive method for finding approximations for Hamilton-Jacobi equations whose L ∞-distance to the viscosity solution is no bigger than a prescribed tolerance. This is done on the simple setting of a one-dimensional model problem with periodic boundary conditions. W ..."

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In this paper, we introduce a new adaptive method for finding approximations for Hamilton-Jacobi equations whose L ∞-distance to the viscosity solution is no bigger than a prescribed tolerance. This is done on the simple setting of a one-dimensional model problem with periodic boundary conditions. We consider this to be a stepping stone towards the more challenging goal of contructing such methods for general Hamilton-Jacobi equations. The method proceeds as follows. On any given grid, the approximate solution is computed by using a well known monotone scheme; then, the quality of the approximation is tested by using an approximate a posteriori error estimate. If the error is bigger than the prescribed tolerance, a new grid is computed by solving a differential equation whose devising is the main contribution of the paper. A thorough numerical study of the method is performed which shows that rigorous error control is achieved, even though only an approximate a posteriori error estimate is used; the method is thus reliable. Furthermore, the numerical study also shows that the method is efficient and that it has an optimal computational

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An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part I: The one-dimensional *steady* *state* *case*

"... In this paper, we introduce a new adaptive method for nding approximations for Hamilton-Jacobi equations whose L1-distance to the viscosity solution is no bigger than a prescribed tolerance. This is done on the simple setting of a one-dimensional model problem with periodic boundary conditions. We c ..."

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In this paper, we introduce a new adaptive method for nding approximations for Hamilton-Jacobi equations whose L1-distance to the viscosity solution is no bigger than a prescribed tolerance. This is done on the simple setting of a one-dimensional model problem with periodic boundary conditions. We consider this to be a stepping stone towards the more challenging goal of contructing such methods for general Hamilton-Jacobi equations. The method proceeds as follows. On any given grid, the approximate solution is computed by using a well known monotone scheme; then, the quality of the approximation is tested by using an approximate a posteriori error estimate. If the error is bigger than the prescribed tolerance, a new grid is computed by solving a dierential equation whose devising is the main contribution of the paper. A thorough numerical study of the method is performed which shows that rigorous error control is achieved, even though only an approximate a posteriori error estimate is used; the method is thus reliable. Furthermore, the numerical study also shows that the method is ecient and that it has an optimal computational complexity. These properties are independent of the value of the tolerance. Finally, we provide extensive numerical evidence indicating that the adaptive method con-verges to an approximate solution that can be characterized solely in terms of the tolerance, the articial viscosity of the monotone scheme and the exact solution.

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Linear-Quadratic Approximation to Unconditionally Optimal Policy: The Distorted *Steady-State**

, 2008

"... This paper establishes that one can generally obtain a purely quadratic approximation to the unconditional expectation of social welfare when the steady-state is distorted. A specific example is provided employing a canonical New Keynesian model. Unlike in the non-distorted steady state case, the ap ..."

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This paper establishes that one can generally obtain a purely quadratic approximation to the unconditional expectation of social welfare when the

*steady-state*is distorted. A specific example is provided employing a canonical New Keynesian model. Unlike in the non-distorted*steady**state**case*###
*Steady-state*

"... and stability analysis of a population balance based nonlinear ice cream crystallization model ..."

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and stability analysis of a population balance based nonlinear ice cream crystallization model

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on *steady-state*

"... Adaptive optics system for investigation of the effect of the aberration dynamics of the human eye ..."

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Adaptive optics system for investigation of the effect of the aberration dynamics of the human eye

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*Steady-state*

"... and stability analysis of a population balance based nonlinear ice cream crystallization model ..."

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and stability analysis of a population balance based nonlinear ice cream crystallization model