Thank you for downloading regularization of inverse problems. Maybe you have knowledge that, people have search hundreds times for their favorite novels like this regularization of inverse problems, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their computer. regularization of inverse problems is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the regularization of inverse problems is universally compatible with any devices to read.

Regularization Of Inverse Problems

We consider the inverse problems of for the fractional Schr\"{o}dinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calder\'{o}n problem in a constructive manner. Secondly, we offer a reconstruction method for an unknown obstacles in a given domain. Our method is independent of the dimension $n\geq 2$ and only requires the background solution of the fractional Schr\"{o}dinger equation.

Monotonicity-based inversion of the fractional Schr\"odinger equation

In this work, we use monotonicity-based methods for the fractional Schrodinger equation with general potentials q in L^\infty(Omega) in a Lipschitz bounded open set Omega \subset R^n in any dimensi...

Monotonicity-based inversion of the fractional schodinger equation ii. general potentials and stability

We consider an inverse problem for the fractional Schrodinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their...

Monotonicity-based Inversion of the Fractional Schrödinger Equation I. Positive Potentials

Static path optimization (SPO) is a foundation of computational intelligence, but in reality, the routing environment is usually time-varying (e.g., moving obstacles, spreading disasters and uncertainties). Thanks to scientific and technical advances in many relevant domains nowadays, changes in the routing environment are often more or less predictable. This study mainly focuses on path optimization in a given dynamic routing environment (POGDRE). A common practice to deal with dynamic routing environment is to conduct online re-optimization (OLRO), i.e., at each time t , environmental parameters are measured/predicted first, and then the best path is re-calculated by resolving SPO based on the newly measured/predicted environmental parameters. In theory, POGDRE is equivalent to time-dependent path optimization (TDPO), which is usually resolved as SPO on a time-expanded hypergraph (TEHG) with a significantly enlarged size. In other words, during a single online run of OLRO-based methods or a single run of TEHG-based methods, the route network is actually fixed and static. Inspired by the multi-agent co-evolving nature reflected in many methods of evolutionary computation, this paper proposes a methodology of co-evolutionary path optimization (CEPO) to resolve the POGDRE. Distinguishing from OLRO and TEHG methods, in CEPO, future routing environmental parameters keep changing during a single run of optimization on a network of original size. In other words, the routing environment co-evolves with the path optimization process within a single run. This paper then reports a ripple-spreading algorithm (RSA) as a realization of CEPO to resolve the POGDRE with both optimality and efficiency. In just a single run of RSA, the optimal actual travelling trajectory can be achieved in a given dynamic routing environment. Simulation results clearly demonstrate the effectiveness and efficiency of the proposed CEPO and RSA for addressing the POGDRE.

Co-Evolutionary path optimization by Ripple-Spreading algorithm

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lame parameters with certain regularity assumptions. In addition, we assume that the Lame parameters belong to a known finite subspace with a priori known bounds and that they fulfill a monotonicity property. The proof relies on a monotonicity result combined with the techniques of localized potentials. To numerically solve the inverse problem, we propose a Kohn-Vogelius-type cost functional over a class of admissible parameters subject to two boundary value problems. The reformulation of the minimization problem via the Neumann-to-Dirichlet operator allows us to obtain the optimality conditions by using the Frechet differentiability of this operator and its inverse. The reconstruction is then performed by means of an iterative algorithm based on a quasi-Newton method. Finally, we give and discuss several numerical examples.

Lipschitz stability estimate and reconstruction of Lam\'e parameters in linear elasticity

In this paper, we consider the inverse problem of recovering an isotropic elastic tensor from the Neumann-to-Dirichlet map. To this end, we prove a Lipschitz stability estimate for Lame parameters ...

Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity

In this paper, we deal with the inverse problem of the shape reconstruction of inclusions in elastic bodies. The main idea of this reconstruction is based on the monotonicity property of the Neumann-to-Dirichlet operator presented in a former article of the authors. Thus, we introduce the so-called standard as well as linearized monotonicity tests in order to detect and reconstruct inclusions. In addition, we compare these methods with each other and present several numerical test examples.

Sarah Eberle

Papers

Lipschitz stability estimate and reconstruction of Lam\'e parameters in linear elasticity

Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity

Shape Reconstruction in Linear Elasticity: Standard and Linearized Monotonicity Method

Shape reconstruction in linear elasticity: standard and linearized monotonicity method

Forest Fire Spreading