Sander, Oliver DUNE – the distributed and unified numerics environment. (English) Zbl 1483.65004 Lecture Notes in Computational Science and Engineering 140. Cham: Springer (ISBN 978-3-030-59701-6/hbk; 978-3-030-59704-7/pbk; 978-3-030-59702-3/ebook). ix, 616 p. (2020). This book is about the Distributed and Unified Numerics Environment for numerical computation using finite element and finite volume methods. A brief review on such methods is given, and how to implement those methods in DUNE based on the Dune module. For instace, the complete implementations of a finite element code are given for the Poisson equation, and a finite volume method for a transport equation.The author discusses the overall structure of Dune, and the functions of modules are discussed. For examples, the grid interface for single-process situations and grids distributed across more than one process are discussed. The dune-localfunctions module is presented for collection of finite element bases on single elements. Numerical quadrature is discussed in the dune-geometry module. A module provides unified access to functions and discrete function spaces. The functions interface follows the approach in the C++ standard library and differentiable functions and functions are defined on finite element grids. The dune-functions module provides various standard bases.In the appendix, the Dune build system is introduced and the complete example program source codes are listed for discussion in the book.Reviewer’s remark: This book is very good for beginners for studying and learning finite element and finite volume methods in Dune. Reviewer: Albert Luo (Edwardsville) Cited in 1 Document MSC: 65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 65-04 Software, source code, etc. for problems pertaining to numerical analysis 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65N08 Finite volume methods for boundary value problems involving PDEs Keywords:finite element method; finite volume method Software:CurvilinearGrid; MRST; DuMuX; UG; VTK; SuperLU; FoamGrid; Gmsh; DUNE-ALUGrid; deal.ii; UMFPACK; DUNE; PETSc; ISTL; Trilinos; ParMETIS; CHOLMOD; PT-Scotch; ALBERTA; gmp; libPTScotch; FEAP PDF BibTeX XML Cite \textit{O. Sander}, DUNE -- the distributed and unified numerics environment. Cham: Springer (2020; Zbl 1483.65004) Full Text: DOI OpenURL