This self-contained book describes 1D and 2D finite element codes and automatic hp-adaptivity strategies that are designed to deliver meshes in the full range of error levels. The book first considers standard 1D elliptic problems and a 1D wave propagation problem. It proceeds to discuss 2D elliptic problems, examining two model problems that are slightly beyond standard-level examples. The author also includes an entire chapter on geometric modeling and mesh generation. The book then focuses on 2D time-harmonic Maxwell equations. A companion CD-ROM containing 1D and 2D codes is included as...

One of the first books to thoroughly discuss the most promising devices for the future, Quantum Computing Devices: Principles, Designs, and Analysis explores contemporary and important aspects of quantum computation, particularly focusing on quantum electronic devices as quantum gates. It presents the analysis, design, and modeling of the major types of quantum computing devices: ion traps, cavity quantum electrodynamics (QED), linear optics, quantum dots, nuclear magnetic resonance (NMR), superconducting quantum interference devices (SQUID), and neutral atom traps. Additional coverage...

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues.
The first part of the book focuses on fundamentals of the 3D theory of hp methods as well as issues that arise when the code is...

Methods for Solving Mixed Boundary Value Problems

An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations.

Straightforward Presentation of Mathematical Techniques

The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic...

A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities.

The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar...

Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice.

After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary...

Presenting Fourier series from the aspect of several variables, this book covers connections between Fourier analysis and partial differential equations. It discusses newly emerging topics, such as the fundamental results on Calderon-Zygmund kernels in multi-dimensions and their relation to Fourier series and integrals, along with Fourier integrals and their applications to uniqueness for two-dimensional trigonometric series. The author explores important applications for the first time through reaction-diffusion equations and Navier-Stokes equations. The text also covers spherical harmonics...

Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems

Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Levy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material.

New to the Second Edition

• Two sections on the Levy type of stochastic integrals and the related stochastic differential equations in...