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PETSc for Partial Differential Equations - Numerical Solutions in C and Python (Paperback)
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PETSc for Partial Differential Equations - Numerical Solutions in C and Python (Paperback)
Series: Software, Environments, and Tools
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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 discretizations and fast solvers for PDEs,
emphasizing practice more than theory. Well-structured examples
lead to run-time choices that result in high solver performance and
parallel scalability. The last two chapters build on the reader’s
understanding of fast solver concepts when applying the Firedrake
Python finite element solver library. 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.
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