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Read e-book online Advanced Topics in Computational Partial Differential PDF

By X. Cai, E. Acklam, H. P. Langtangen (auth.), Hans Petter Langtangen, Aslak Tveito (eds.)

ISBN-10: 3540014381

ISBN-13: 9783540014386

The e-book is appropriate for readers with a historical past in simple finite point and finite distinction tools for partial differential equations who desires light introductions to complex subject matters like parallel computing, multigrid equipment, and exact equipment for platforms of PDEs. The target of all chapters is to *compute* options to difficulties, therefore algorithmic and software program matters play a important position. All software program examples use the Diffpack programming atmosphere, so that you can benefit from those examples a few event with Diffpack is needed. There also are a few chapters overlaying whole functions, i.e., the way in which from a version, expressed as platforms of PDEs, via discretization equipment, algorithms, software program layout, verification, and computational examples.

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Additional info for Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

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Suppose the solution process involves an iterative linear system solver, then the most computation intensive operations viewed at the level of matrices and vectors are: (i) calculation of element matrices and vectors , and (ii) solution of the resulting linear system of equations. Roughly speaking, the parallelization starts with partitioning the global finite element grid into a set of smaller subgrids to be hosted by different processors of a parallel computer. It is important to note that global matrices and vectors need not to be constructed physically.

To increase the human efficiency in developing parallel computer codes, we should develop a software environment where the programmer can concentrate on the principal steps of parallel algorithms, rather than on MPI-specific details. A desired situation will be that a programmer can start with developing a sequential solver and then in just a few steps transform this solver to a parallel version. Realization of such a software environment is indeed possible and requires a layered design of software abstractions, where all explicit MPI calls are hidden in the most primitive layer, and where the interface to message passing tools is simple and adapted to the programming standard of sequential solvers.

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Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming by X. Cai, E. Acklam, H. P. Langtangen (auth.), Hans Petter Langtangen, Aslak Tveito (eds.)

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