This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequencies\temporal data to improve stability and numerical resolution. There are also numerous ...

This book guides undergraduate students in the use of Maxima—a computer algebra system—in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook.When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that st...

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader wit...

Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown.Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the ...

This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, wh...

Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker d...

This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstr...

This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions.The book is mathematical, poising problems in...

This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects.The goal of numerical simulations using quantum mechanical models in the dev...

One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite vo...

This volume comprises a carefully selected collection of articles emerging from and pertinent to the 2010 CFL-80 conference in Rio de Janeiro, celebrating the 80th anniversary of the Courant-Friedrichs-Lewy (CFL) condition. A major result in the field of numerical analysis, the CFL condition has influenced the research of many important mathematicians over the past eight decades, and this work is meant to take stock of its most important and current applications.The Courant–Fri...

Leonardo wrote, “Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics”; replace “Mechanics” by “Fluid mechanics” and here we are.- From the Preface to the Second EditionAlthough the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows ...