# Haut PDF Iterative Methods for Model Reduction by Domain Decomposition

### Iterative Methods for Model Reduction by Domain Decomposition

**model**based on proper orthogonal

**decomposition**(POD) [4] to solve the ...solution

**by**a small number of unknowns that are the coefficients of an appropriate Galerkin ...solved

**for**is ...

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### Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

**for**improvement of this class of

**methods**.

**For**instance,

**by**combining cleverly several integral operators, one could expect the same gain that has been achieved with Pad´ e-like operators ...

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### Model order reduction methods for parameter-dependent equations -- Applications in Uncertainty Quantification.

**model**order

**reduction**: the use of a preconditioner P (ξ) ≈ A(ξ) −1 is necessary to obtain accurate ...defined

**by**a projection method based on the Frobenius ...]

**for**an ...

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### Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media

**for**the mass conservation of each component and the multiphase Darcy ...allow

**for**large time ...solution

**by**an

**iterative**Krylov method such as GMRES or BiCGStab requires the ...

164

### Large-scale frequency-domain seismic wave modeling on h-adaptive tetrahedral meshes with iterative solver and multi-level domain-decomposition preconditioners

**methods**on uniform Cartesian grid (Op- erto et ...offered

**by**unstructured meshes to adapt the size of the elements to the local wavelengths (the so-called h-adaptivity) offers a good ...

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### Dual Norm Based Iterative Methods for Image Restoration

**model**(25) proposed

**by**Le et al, we also observe that the proposed

**iterative**method gives much sharper and cleaner ...the

**iterative**algorithm to image deblurring via (cartoon + ...

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### Galerkin-free model reduction for fluid-structure interaction using proper orthogonal decomposition

**for**this FSI system: first, the traditional Galerkin projection of the Navier-Stokes equations on the POD time invariant modes (or space modes) when the computation

**domain**is time dependent, which is ...

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### Model Order Reduction in Hyperelasticity: A Proper Generalized Decomposition Approach

**methods**(those designed

**for**data lying on a manifold) are always difficult to ...generalized

**decomposition**(PGD)

**methods**, on the contrary, arose recently as a gener- alization of POD ...

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### Domain decomposition for coupling finite and boundary element methods in EEG

**for**the isotropic case,

**for**pure and coupled ...sphere

**model**[2],

**for**both isotropic and anisotropic skull ...1.0}

**for**the isotropic ...done

**for**5 dipoles oriented in ...

5

### Corners and stable optimized domain decomposition methods for the Helmholtz problem

**iterative**DDM ...Both

**methods**are shown to be convergent using a technique based on a suitable quadratic energy defined on the skeleton of the mesh ...the

**iterative**solution of the DDM and the ...

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### Prediction of apparent properties with uncertain material parameters using high-order fictitious domain methods and PGD model reduction

**domain**method ap- proximation which enables to avoid the meshing burden with such complex geometries, and (ii) a

**model**

**reduction**technique based on the Proper Generalized ...

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### Time-domain simulation of large electric power systems using domain-decomposition and parallel processing methods

**domain**is to minimize the interfaces between the ...allow

**for**lower communication requirements and a simpler handling of interface ...defined

**by**geometric ...used.

**For**a system with N ...

211

### Two-Level Domain Decomposition Methods for Highly Heterogeneous Darcy Equations. Connections with Multiscale Methods

**for**its use in subsurface modeling. As explained in Section 2.2, the rationale behind this coarse space is ...

24

### Domain decomposition methods to model heat exchanges between a well and a rock mass

**by**

**model**(black marks) compared to availble data (grey marks) - flow rate (black line) is imposed in the ...preconditionned

**by**an Algebraic MultiGrid (AMG) method

**for**the rock linear ...

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### A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

**for**the resulting large, sparse and omplex oe- ients algebrai systems. ...

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### Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves with High Order Whitney Forms

**by**the lack of preconditioning of the

**iterative**solver [15]. Without it, the iteration count ...

4

### Efficient high order and domain decomposition methods for the time-harmonic Maxwell's equations

**by**doctors thanks to an image of the brain displaying the values of this ...solver

**for**the direct problem is ...application,

**for**a precise detection of the stroke and the continuous monitoring of ...

153

### On Domain Decomposition Methods with optimized transmission conditions and cross-points

**By**definition, one has that Π∂ n = ∂ n ...key

**for**this ...the

**iterative**DDM already quoted in the literature [3, 6, 9, 14, 17, 20, 21, 22, 8] can be recast under the form ...DDM

**for**the ...

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### Model reduction based on Proper Generalized Decomposition for the Stochastic steady incompressible Navier-Stokes equations

**by**classical deterministic solvers, thus making the proposed algorithm a partially non intrusive ...proposed

**for**the reconstruction of an approximation of the pressure ﬁeld, the random velocity ﬁeld ...

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### Effective Transmission Conditions for Domain Decomposition Methods applied to the Time-Harmonic Curl-Curl Maxwell's equations

**for**the simulation of many modern devices we have become used to in everyday ...hampered

**by**two fundamental problems: first, in the high frequency regime, very fine meshes need to be used in ...

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