This book presents a systematic methodology for the development of parallel multi-physics models and its implementation in geophysical and biomedical applications. The methodology includes conservative discretization methods for partial differential equations on general meshes, as well as data structures and algorithms for organizing parallel simulations on general meshes. The structures and algorithms form the core of the INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) platform for the development of parallel models on general meshes. The authors consider applications for addressing specific geophysical and biomedical challenges, including radioactive contaminant propagation with subsurface waters, reservoir simulation, and clot formation in blood flows. The book gathers all the components of this methodology, from algorithms and numerical methods to the open-source software, as well as examples of practical applications, in a single source, making it a valuable asset for applied mathematicians, computer scientists, and engineers alike.

This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.

This book constitutes the proceedings of the 16th International Conference on Parallel Computing Technologies, PaCT 2021, which was held during September 13-18, 2021. The conference was planned to take place in Kaliningrad, Russia, but changed to an online event due to the COVID-19 pandemic. The 24 full and 12 short papers included in this book were carefully reviewed and selected from 62 submissions. They were organized in topical sections as follows: parallel programming methods and tools; applications; memory-efficient data structures; experimental studies; job management; essential algorithms; computing services; and cellular automata.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.

This book constitutes the refereed post-conference proceedings of the 6th Russian Supercomputing Days, RuSCDays 2020, held in Moscow, Russia, in September 2020.* The 51 revised full and 4 revised short papers presented were carefully reviewed and selected from 106 submissions. The papers are organized in the following topical sections: parallel algorithms; supercomputer simulation; HPC, BigData, AI: architectures, technologies, tools; and distributed and cloud computing. * The conference was held virtually due to the COVID-19 pandemic.

This volume contains 25 review articles by experts which provide up-to-date information about the recent progress in computational fluid dynamics (CFD). Due to the multidisciplinary nature of CFD, it is difficult to keep up with all the important developments in related areas. CFD Review 2010 would therefore be useful to researchers by covering the state-of-the-art in this fast-developing field.