Raymond J. Spiteri - Böcker

These proceedings present a curated collection of innovative approaches to tackling challenging problems in applied mathematics. These problems, often marked by instability, inaccuracy, and high computational cost, remain at the forefront of mathematical research due to their difficulty. Addressing this demand, the contributions in this volume offer robust numerical methods designed to improve the accuracy and efficiency of their solutions.The book originates from the Go20 Conference 2023, where established experts and emerging researchers explored cutting-edge methodologies. The discussions captured here situate new advancements within a broader historical and theoretical context, providing a well-rounded perspective on these pressing mathematical challenges.Topics covered include:Ordinary Differential Equations (ODEs) with singularitiesMulti-dimensional and multi-rate systems of Partial Differential Equations (PDEs)High-index Differential-Algebraic Equations (DAEs)Inverse and optimal control problemsThis collection is a valuable resource for researchers and practitioners working on these or related topics. It offers comprehensive analyses and practical insights that bridge foundational principles with modern numerical innovations.

Scientific computing is essential for tackling complex problems across many domains—but how can scientists develop high-performance and high-quality software that scales efficiently? This book serves as an accessible introduction to extreme-scale computing, specifically designed for domain scientists who may not have formal computer science training but need to harness the power of C++ and parallel computing for large-scale applications.The book begins by covering the fundamentals of scientific computing software management, including essential tools like Linux, Git, and CMake, before diving into a detailed exploration of C++ for extreme-scale computing. Readers familiar with languages like Python will gain the necessary skills to transition to C++ and build scalable, efficient software.  Beyond basic programming, this book delves into hardware-aware computing, teaching readers how to optimize software performance by understanding the underlying architecture of modern computational systems. It then introduces parallel computing techniques, covering MPI for distributed memory parallelism, shared memory parallelism, CUDA for GPU programming, and Kokkos for performance portability.Further chapters focus on efficient I/O, debugging, and profiling, which all address aspects of the critical challenge of performance optimization in extreme-scale computing. The book concludes with an overview of popular libraries for extreme-scale computing, equipping readers with the tools they need to solve real-world computational problems.  With a balance of theory, practical applications, and illustrative case studies, this book provides domain scientists with a comprehensive roadmap to mastering extreme-scale computing and developing highly parallel and performant software.

This volume presents a curated collection of contributions from the Go20 Conference on Scientific Computing and Software, held May 20–24, 2024, in Gozo, Malta. Go20 is an exclusive, invitation-only event limited to 20 participants, designed to foster deep exchange among leading experts from academia, industry, and the public sector. With no parallel sessions and 45-minute talks by every attendee, the conference offers an intensive forum for sharing cutting-edge research.All papers included in this proceedings underwent rigorous peer review. The topics reflect the forefront of scientific computing, emphasizing both theoretical advances and their realization in software—bridging abstract algorithms with practical implementation. Areas of focus include:Perturbations and backward error analysisDomain decomposition techniquesSuperconvergence of non-stiffly accurate implicit Runge–Kutta methods for index-2 DAEsParallel-in-time spectral deferred correction and collocation methodsComputational approaches for physiological dysfunctions and clinical medicineParameter estimation for multidimensional stochastic differential equationsNovel operator-splitting and fractional-step methods for real and complex PDEsThese contributions advance the rapidly evolving field of scientific computing, addressing challenges with profound societal impact—from healthcare and medicine to climate modeling and data-driven decision-making. By highlighting the interplay between theory and software, this book serves as a valuable resource for researchers seeking insight into state-of-the-art methods and their practical applications.Researchers and practitioners in scientific computing, numerical analysis, and applied mathematics—both academic and non-academic—will find this volume an essential reference for the latest developments in algorithms and software for differential equations and linear systems.

Focusingon five main groups of interdisciplinary problems, this book covers a widerange of topics in mathematical modeling, computational science and appliedmathematics. It presents a wealth of new results in the development of modelingtheories and methods, advancing diverse areas of applications and promotinginterdisciplinary interactions between mathematicians, scientists, engineersand representatives from other disciplines.Thebook offers a valuable source of methods, ideas, and tools developed for avariety of disciplines, including the natural and social sciences, medicine,engineering, and technology. Original results are presented on both thefundamental and applied level, accompanied by an ample number of real-worldproblems and examples emphasizing the interdisciplinary nature and universalityof mathematical modeling, and providing an excellent outline of today’schallenges. Mathematical modeling,with applied and computational methods and tools, plays a fundamental role inmodern science and engineering. It provides a primary and ubiquitous tool inthe context making new discoveries, as well as in the development of newtheories and techniques for solving key problems arising in scientific andengineering applications.Thecontributions, which are the product of two highly successful meetingsheld jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid LaurierUniversity in June 2015, i.e. the International Conference on AppliedMathematics, Modeling and Computational Science, and the Annual Meeting of theCanadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interestedin a broader overview of the methods, ideas and tools involved in mathematicaland computational approaches developed for other disciplines, including thenatural and social sciences, engineering and technology.