Adaptive Mesh Refinement Theory And Applications

Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

The papers presented here describe research to improve the general understanding of the application of SAMR to practical problems, to identify issues critical to efficient and effective implementation on high performance computers and to stimulate the development of a community code repository for software including benchmarks to assist in the evaluation of software and compiler technologies. The ten chapters have been divided into two parts reflecting two major issues in the topic: programming complexity of SAMR algorithms and the applicability and numerical challenges of SAMR methods.

Therefore, they are excellent computer analysis and design (CAD) tools. The book starts by introducing the FDTD technique, along with challenges related to its application to the analysis of real-life microwave and optical structures. It then proceeds to developing an adaptive mesh refinement method based on the use of multiresolution analysis and, more specifically, the Haar wavelet basis. Furthermore, a new method to embed a moving adaptive mesh in FDTD, the dynamically adaptive mesh refinement (AMR) FDTD technique, is introduced and explained in detail. To highlight the properties of the theoretical tools developed in the text, a number of applications are presented, including: Microwave integrated circuits (microstrip filters, couplers, spiral inductors, cavities); Optical power splitters, Y-junctions, and couplers; Optical ring resonators; Nonlinear optical waveguides.

This volume collects the most important contributions from four minisymposia from ICIAM 2019. The papers highlight cutting-edge applications of Cartesian CFD methods and describe the employed algorithms and numerical schemes. An emphasis is laid on complex multi-physics applications like magnetohydrodynamics, combustion, aerodynamics with fluid-structure interaction, solved with various discretizations, e.g. finite difference, finite volume, multiresolution or lattice Boltzmann CFD schemes. Software design aspects and parallelization challenges are also considered. The book is addressed to graduate students and scientists in the fields of applied mathematics and computational engineering.

This book constitutes the thoroughly refereed post-workshop proceedings of the First and the Second International Workshop on OpenMP, IWOMP 2005 and IWOMP 2006, held in Eugene, OR, USA, and in Reims, France, in June 2005 and 2006 respectively. The first part of the book presents 16 revised full papers carefully reviewed and selected from the IWOMP 2005 program and organized in topical sections on performance tools, compiler technology, run-time environment, applications, as well as the OpenMP language and its evaluation. In the second part there are 19 papers of IWOMP 2006, fully revised and grouped thematically in sections on advanced performance tuning aspects of code development applications, and proposed extensions to OpenMP.

The papers presented here describe research to improve the general understanding of the application of SAMR to practical problems, to identify issues critical to efficient and effective implementation on high performance computers, and to stimulate the development of a community code repository for software including benchmarks to assist in the evaluation of software and compiler technologies. The ten chapters have been divided into two parts: programming complexity of SAMR algorithms and the applicability and numerical challenges of SAMR methods.