Schwarz methods
Optimized Schwarz methods for Maxwell's equations
... convergent Schwarz method for the Helmholtz equation, where the classical overlapping Schwarz algorithm is not ...classical Schwarz method is rather slow and too strongly dependent on the size of the ...
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Optimized schwarz methods for Maxwell equations with discontinuous coefficients
... optimized Schwarz methods for Maxwell’s equations in hetero- geneous media with discontinuous coefficients, and show that the discontinuities need to be taken into account in the transmission conditions in ...
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Schwarz methods for second order Maxwell equations in 3D with coefficient jumps
... Classical Schwarz methods need in general overlap to converge, but in the case of hyperbolic problems, they can also be convergent without overlap, see ...classical Schwarz method without overlap ...
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Asymptotic analysis of optimized Schwarz methods for Maxwell's equations with discontinuous coefficients
... optimized Schwarz methods which take the physics of the underlying problem into account, one can not just obtain robustness in terms of the jumps in the coefficients, but even benefit from them, obtaining ...
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Optimized Schwarz methods for curl-curl time-harmonic Maxwell's equations
... iterative methods. Domain decomposition methods are currently most promising: following the first provably convergent method in [4], various optimized Schwarz methods were developed over the ...
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DG discretization of optimized Schwarz methods for Maxwell's equations
... (DG) methods have seen rapid growth and are widely used in various application domains (see [13] for an historical intro- ...optimized Schwarz methods can be ...optimized Schwarz DD ...
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Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations
... optimized Schwarz methods, provided that the co- efficient jumps are aligned with the interfaces, and the jumps are taken into account in an appropriate way in the transmission ...
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Can the discretization modify the performance of Schwarz methods?
... Optimized Schwarz methods have been analyzed thoroughly for the positive definite Helmholtz equation at the continuous level in Gander [2006], and extensive numerical tests have been presented which ...
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An introduction to multitrace formulations and associated domain decomposition solvers
... decomposition methods called optimal Schwarz methods, see [18, 10, 11, 12, 13], and [9] for an overview with further ...Optimal Schwarz methods use Dirichlet to Neumann operators in ...
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Effective transmission conditions for domain decomposition methods applied to the time-harmonic curl-curl Maxwell's equations
... overlapping Schwarz methods was de- veloped for scalar partial differential equations, namely the optimized Schwarz ...These methods are based on a classical overlapping domain decom- ...
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Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations
... For overlapping domain decomposition preconditioners, a similar idea was introduced in the case of Darcy equations in [GE10a, GE10b]. The authors of [NXD10] consider also the hetero- geneous Darcy equation and presented ...
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Norm Inequalities for Sequences of Operators Related to the Schwarz Inequality
... Some norm inequalities for sequences of linear operators defined on Hilbert spaces that are related to the classical Schwarz inequality are given.. Applications for vector inequalities a[r] ...
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The complete AdS3 ×S3 × T4 worldsheet S matrix
... the coset to facilitate the computations. The coset action is obtained from a Green-Schwarz action [66] by fully fixing the kappa symmetry to the so-called coset gauge. While it is use- ful in the study of the ...
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Extensions of the Hardy Littlewood inequalities for Schwarz symmetrization
... Our main results are Proposition 4.1, which establishes inequality 1.1 for all symmetrizable functions provided that H satisfies appropriate conditions, and Theorem 4.4 which establishes [r] ...
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Schwarz lemma involving the boundary fixed point
... On the other hand, Schwarz lemma at the boundary is also an active topic in complex analysis, various interesting results have been obtained [–]. Before summarizing these results, it is necessary to give some ...
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Schwarz Pick type estimates for the hyperbolic derivative
... ρ f ∗ (0), f ∗ (z) ≤ 2ρ(0,z) ∀ z ∈ Δ . (1.7) In the next section of this paper, we employ a procedure which yields simple proofs of Theorems 1.3 and 1.4 and extends these results. In particular, Theorem 1.4 is not appli- ...
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Generalizations of Cauchy Schwarz inequality in unitary spaces
... The Cauchy-Schwarz inequality is one of the most important inequalities in mathemat- ics. To date, a large number of generalizations and refinements of the inequalities (.) and (.) have been investigated in the ...
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A Potpourri of Schwarz Related Inequalities in Inner Product Spaces
... The main aim of the present paper is to point out other results in connection with both the quadratic and simple forms of the Schwarz inequality. As applications, some reverse results for the generalised triangle ...
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Some Results Related to the Cauchy-Bunyakovsky-Schwarz Inequality
... DRAGOMIR, Advances in Inequalities of the Schwarz, Gr¨ uss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., NY, 2005.. [5] Y.-C.[r] ...
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