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This book provides a snapshot of the state of the art of the
rapidly evolving field of integration of geometric data in finite
element computations. The contributions to this volume, based on
research presented at the UCL workshop on the topic in January
2016, include three review papers on core topics such as fictitious
domain methods for elasticity, trace finite element methods for
partial differential equations defined on surfaces, and Nitsche's
method for contact problems. Five chapters present original
research articles on related theoretical topics, including Lagrange
multiplier methods, interface problems, bulk-surface coupling, and
approximation of partial differential equations on moving domains.
Finally, two chapters discuss advanced applications such as crack
propagation or flow in fractured poroelastic media. This is the
first volume that provides a comprehensive overview of the field of
unfitted finite element methods, including recent techniques such
as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian
techniques. It is aimed at researchers in applied mathematics,
scientific computing or computational engineering.
Systems of linear equations are ubiquitous in numerical analysis
and scientific computing. and iterative methods are indispensable
for the numerical treatment of such systems. This book offers a
rigorous introduction to fundamental iterative methods for systems
of linear algebraic equations. The book distinguishes itself from
other texts on the topic by providing a straightforward yet
comprehensive analysis of the Krylov subspace methods, approaching
the development and analysis of algorithms from various
perspectives, and going beyond the standard description of
iterative methods by connecting them in a natural way to the idea
of preconditioning. The book supplements standard texts on
numerical mathematics for first-year graduate and advanced
undergraduate courses and is suitable for advanced graduate classes
covering numerical linear algebra and Krylov subspace and multigrid
iterative methods. It will be useful to researchers interested in
numerical linear algebra and engineers who use iterative methods
for solving large algebraic systems.
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