DUNE – the distributed and unified numerics environment. (English) Zbl 07283204

Sander, Oliver

Lecture Notes in Computational Science and Engineering 140. Cham: Springer (ISBN 978-3-030-59701-6/hbk; 978-3-030-59702-3/ebook). ix, 616 p. (2020).

This book is about the Distributed and Unified Numerics Environment for numerical computation in finite element and finite volume methods. A brief review on such finite element and finite volume methods is given, and presented is how to implementation of those methods in the 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 dsicussed. 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.The 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 Appendix, the Dune build system is introduced and all complete example program source codes are listed for discussion in the book.

Reviewer: Albert Luo (Edwardsville)

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:

Dune; finite element method; finite volume method

Software:

ALBERTA; CHOLMOD; CurvilinearGrid; deal.ii; DuMuX; DUNE; DUNE-ALUGrid; FEAP; FoamGrid; gmp; Gmsh; ISTL; libPTScotch; MRST; ParMETIS; PETSc; PT-Scotch; SuperLU; Trilinos; UG; UMFPACK; VTK