Ebook: Advances in mathematical methods and high performance computing

This special volume of the conference will be of immense use to the researchers and academicians. In this conference, academicians, technocrats and researchers will get an opportunity to interact with eminent persons in the field of Applied Mathematics and Scientific Computing. The topics to be covered in this International Conference are comprehensive and will be adequate for developing and understanding about new developments and emerging trends in this area. High-Performance Computing (HPC) systems have gone through many changes during the past two decades in their architectural design to satisfy the increasingly large-scale scientific computing demand. Accurate, fast, and scalable performance models and simulation tools are essential for evaluating alternative architecture design decisions for the massive-scale computing systems. This conference recounts some of the influential work in modeling and simulation for HPC systems and applications, identifies some of the major challenges, and outlines future research directions which we believe are critical to the HPC modeling and simulation community.;Intro; Preface; Contents; Part I Mathematical Modeling, Applications, and Theoretical Foundations; Canonical Duality-Triality Theory: Unified Understanding for Modeling, Problems, and NP-Hardness in Global Optimizationof Multi-Scale Systems; 1 Introduction and Motivation; 2 Multi-Scale Modeling and Properly Posed Problems; 2.1 Objectivity, Isotropy, and Symmetry in Modeling; 2.2 Subjectivity, Symmetry Breaking, and Well-Posed Problem; 2.3 Management Optimization; 2.4 Nonconvex Analysis and Boundary-Value Problems; 2.5 Lagrangian Mechanics and Initial-Value Problems