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With a focus on 1D and 2D problems, the first volume of Computing
with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts
and logic governing 3D code and implementation. Taking the next
step in hp technology, Volume II Frontiers: Three-Dimensional
Elliptic and Maxwell Problems with Applications presents the
theoretical foundations of the 3D hp algorithm and provides
numerical results using the 3Dhp code developed by the authors and
their colleagues. The first part of the book focuses on
fundamentals of the 3D theory of hp methods as well as issues that
arise when the code is implemented. After a review of
boundary-value problems, the book examines exact hp sequences,
projection-based interpolation, and De Rham diagrams. It also
presents the 3D version of the automatic hp-adaptivity package, a
two-grid solver for highly anisotropic hp meshes and goal-oriented
Krylov iterations, and a parallel implementation of the 3D code.
The second part explores several recent projects in which the 3Dhp
code was used and illustrates how these applications have greatly
driven the development of 3D hp technology. It encompasses acoustic
and electromagnetic (EM) scattering problems, an analysis of
complex structures with thin-walled components, and challenging
simulations of logging tools. The book concludes with a look at the
future of hp methods. Spearheaded by a key developer of this
technology with more than 20 years of research in the field, this
self-contained, comprehensive resource will help readers overcome
the difficulties in coding hp-adaptive elements.
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