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"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." [Publisher]

Differential equations, Partial --- Équations aux dérivées partielles --- Numerical analysis. --- Analyse numérique. --- Parallel programming (Computer science) --- Programmation parallèle (informatique) --- C (Computer program language) --- C (langage de programmation) --- Python (Computer program language) --- Python (langage de programmation) --- Computer programs. --- Logiciels. --- Équations aux dérivées partielles --- Analyse numérique. --- Programmation parallèle (informatique)