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Multilevel Adaptive Methods for Partial Differential Equations (Paperback)
Loot Price: R1,503
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Multilevel Adaptive Methods for Partial Differential Equations (Paperback)
Series: Frontiers in Applied Mathematics, No. 6
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A practical handbook for understanding and using fast adaptive
composite grid (FAC) methods for discretization and solution of
partial differential equations (PDEs). Contains fundamental
concepts. These so called FAC are characterized by their use of a
composite grid, which is nominally the union of various uniform
grids. FAC is capable of producing a composite grid with tailored
resolution, and a corresponding solution with commensurate
accuracy, at a cost proportional to the number of composite grid
points. Moreover, special asynchronous versions of the fast
adaptive composite grid methods (AFAC) studied here have seemingly
optimal complexity in a parallel computing environment. Most of the
methods treated in this book were discovered only within the last
decade, and in many cases their development is still in its
infancy. While this book is therefore not meant to be
comprehensive, it does provide a theoretical and practical guide to
multilevel adaptive methods and relevant discretization techniques.
It also contains new material, which is included to fill in certain
gaps and to expose new avenues of research. Also, because adaptive
refinement seems to demand a lot of attention to philosophical
issues, personal perspectives are often brought freely into the
discussion.
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