Titlebook: Numerical Solution of Elliptic Differential Equations by Reduction to the Interface; Boris N. Khoromskij,Gabriel Wittum Book 2004 Springer

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,Discrete Poincaré-Steklov Mappings for Biharmonic and Lamé Equations,in ideas on an asymptotically optimal Schur complement interface reduction for the Lamé equation on polygonal domains. The approach is based on using special Poincaré-Steklov operators associated with the biharmonic and Stokes equations.

unstable-angina

Interface Reduction for the Stokes Equation,ion may be applied to model a slow flow of viscous incompressible fluid and also in iterative methods for solving the Navier-Stokes and the nonstationary Stokes problems. Efficient finite element multigrid method for the Stokes and Navier-Stokes equations by using transforming smoothers was developed in [187, 189] see also recent results in [26].

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Iterative Substructuring Methods,We shall consider the equation . where .: . → . is a symmetric positive definite (s.p.d.) operator with respect to the inner product (·,·) on the finite dimensional vector space ., . = .. Let .: . → . be another s.p.d. operator. We consider . iterative methods

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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface978-3-642-18777-3Series ISSN 1439-7358 Series E-ISSN 2197-7100

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Boris N. Khoromskij,Gabriel WittumIncludes supplementary material:

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eper and farther than professional work in probing the consequences of a radical design hypothesis. Within academia architects can be more experimental. They can afford to be more principled and more self-critical, avoiding pragmatic compromises. The creative work of the Zaha Hadid Vienna studio testifies to this.

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Book 2004and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the bo

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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface