PETSc for partial differential equations : numerical solutions in C and Python / Ed Bueler.

Format:

Book

Author/Creator:

Bueler, Edward L. (Edward Lee), author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Software, environments, tools.

Software, environments, and tools

Language:

English

Subjects (All):

Differential equations, Partial--Computer programs.

Differential equations, Partial.

Numerical analysis.

Parallel programming (Computer science).

C (Computer program language).

Python (Computer program language).

Physical Description:

1 online resource (xv, 391 pages) : illustrations.

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2021]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton's method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations: addresses both discretization and fast solvers for PDEs; emphasizes practice more than theory; contains well-structured examples, with advice on run-time solver choices; demonstrates how to achieve high performance and parallel scalability; and builds on the reader's understanding of fast solver concepts when applying the Firedrake Python finite element solver library in the last two chapters. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Contents:

Getting started with PETSc

Finite-dimensional linear systems

Poisson equation on a structured grid

Nonlinear equations by Newton's method

Time-stepping

Preconditioners for PDEs

Optimal solvers for elliptic PDEs

Parallel scaling

Finite element method I : Nonlinear optimization

Finite element method II : Naive and unstructured

Advection without, and then with, diffusion

Inequality constraints

Finite element method III : Firedrake and DMPlex

Stokes equations (with Firedrake).

Notes:

Includes bibliographical references (pages 373-381) and index.

Description based on title page of print version.

ISBN:

1-61197-631-6

OCLC:

1162210360

Publisher Number:

SE31 SIAM