Inverse Methods

This volume examines some recent advances in inverse problems, new aspects of their mathematical modeling of inverse problems regarding in relation to their applications in physical systems and used the computational methods used.

In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS). These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach.

This book describes unified image-based measurement methods (theories, numerical methods, and algorithms) to determine the important physical quantities of complex flows in engineering and natural systems, including velocity, pressure, temperature, heat transfer, and skin friction. It presents a systematical study of the inverse problems in global flow diagnostics in a unified framework of the variational formulations. The authors further illustrate the main physical quantities in fluid mechanics, including velocity, pressure, skin friction and surface heat flux, extracted from flow visualization images obtained in experiments and observations. The developed methods are applicable in various image-based flow measurements in diverse disciplines ranging from fluid mechanics/aerodynamics to plenary sciences.

This second edition addresses the question of which finite groups occur as Galois groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K, as well as its finite epimorphic images, generally referred to as the inverse problem of Galois theory.

This textbook provides a comprehensive and didactic introduction from the basics to the current state of the art in the field of EEG/MEG source reconstruction. Reconstructing the generators or sources of electroencephalographic and magnetoencephalographic (EEG/MEG) signals is an important problem in basic neuroscience as well as clinical research and practice. Over the past few decades, an entire theory, together with a whole collection of algorithms and techniques, has developed.

This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics.

This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems.