Titlebook: Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations; Tarek Poonithara Abraham Mathew Book 2008 Sprin

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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

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Multilevel and Local Grid Refinement Methods,ulated using multigrid methodology [BR22, HA4, HA2, BR36]. Multilevel preconditioners can yield optimal order performance, like multigrid methods, however, they are convergent only with Krylov space acceleration.

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Variational Inequalities and Obstacle Problems,ical finance (option pricing) [CR2, EL, WI10, WI11]. Even when the underlying elliptic (or parabolic) equation is linear, an obstacle problem is . due to the unknown region of . between the solution and the obstacle. However, once the contact set is known, the problem is linear on its complementary set.

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1439-7358 tial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. The topics discusse

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Lubnaa Hossenbaccus,Sarah Garvey,Anne Ellisrs and Krylov algorithms. Applications to Navier-Stokes equations, mixed formulations of elliptic equations, and to optimal control problems, are described in Chaps. 10.6, 10.7 and 10.8, respectively. For a more detailed discussion of saddle point problems, readers are referred to [CI4, GI3, BE12].

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Lubnaa Hossenbaccus,Sarah Garvey,Anne Ellisexpected parallel computation time and speed up when implementing a domain decomposition preconditioner on an idealized parallel computer architecture. We outline . estimate for this using idealized models for the computational time and inter-processor data transfer times.

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