Parallel Finite Volume Computation on General Meshes, 1st ed. 2020

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.

A corresponding member of the Russian Academy of Sciences, Professor Yuri Vassilevski is the Deputy Director of the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; the Head of the Department of Computational Technologies and Modelling in Geophysics and Biomathematics at Moscow Institute of Physics and Technology; the Head of the Laboratory of Mathematical Modelling in Medicine at Sechenov Univiersity, Professor at Lomonosov Moscow State University; Managing Editor of the Russian Journal of Numerical Analysis and Mathematical Modelling; Editor of the International Journal for Numerical Methods in Biomedical Engineering and the Journal on Computational Mathematics and Mathematical Physics, and a reviewer for over twenty scientific journals including the Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, and the SIAM Journal on Scientific Computing. He was the PIin the Russian Science Foundation Project “Multiscale modeling of blood flow system in personalized medical technologies of cardiology, vascular neurology, oncology,” 2014–2018 (25 researchers), and in the ExxonMobil-INM Project “Parallel iterative solution of linear systems on multi-core clusters,” 2013–2017 (9 researchers). He is the author or co-author of over one hundred journal papers, three monographs, and two textbooks. His research interests include the theory of quasi-optimal meshes, mesh generation and adaptation, iterative methods for PDEs, discretization methods for PDEs, reservoir simulation, computational fluid dynamics, and computational hemodynamics.

Dr. Kirill Terekhov is a Researcher at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, and former postdoctoral scholar at Stanford University. He was the main developer of the INMOST library, reservoir simulator