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Dive into the research topics where Radek Tezaur is active.

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Featured researches published by Radek Tezaur.


Numerische Mathematik | 2000

On the Convergence of a Dual-Primal Substructuring Method

Jan Mandel; Radek Tezaur

Summary. In the Dual-Primal FETI method, introduced by Farhat et al. [5], the domain is decomposed into non-overlapping subdomains, but the degrees of freedom on crosspoints remain common to all subdomains adjacent to the crosspoint. The continuity of the remaining degrees of freedom on subdomain interfaces is enforced by Lagrange multipliers and all degrees of freedom are eliminated. The resulting dual problem is solved by preconditioned conjugate gradients. We give an algebraic bound on the condition number, assuming only a single inequality in discrete norms, and use the algebraic bound to show that the condition number is bounded by


Journal of Computational Acoustics | 2005

FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING

Charbel Farhat; Philip Avery; Radek Tezaur; Jing Li

C(1+\log^2(H/h))


International Journal for Numerical Methods in Engineering | 1999

THEORETICAL COMPARISON OF THE FETI AND ALGEBRAICALLY PARTITIONED FETI METHODS, AND PERFORMANCE COMPARISONS WITH A DIRECT SPARSE SOLVER

Daniel J. Rixen; Charbel Farhat; Radek Tezaur; Jan Mandel

for both second and fourth order elliptic selfadjoint problems discretized by conforming finite elements, as well as for a wide class of finite elements for the Reissner-Mindlin plate model.


SIAM Journal on Scientific Computing | 1999

Two-grid Method for Linear Elasticity on Unstructured Meshes

Petr Vanek; Marian Brezina; Radek Tezaur

A dual-primal variant of the FETI-H domain decomposition method is designed for the fast, parallel, iterative solution of large-scale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence of this iterative solution method, named here FETI-DPH, is shown to scale with the problem size, the number of subdomains, and the wave number. Its solution time is also shown to scale with the problem size. CPU performance results obtained for the acoustic signature analysis in the mid-frequency regime of mockup submarines reveal that the proposed FETI-DPH solver is significantly faster than the previous generation FETI-H solution algorithm.


Inverse Problems | 2002

On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method

Charbel Farhat; Radek Tezaur; Rabia Djellouli

In this paper, we prove that the AlgebraicA-FETI method corresponds to one particular instance of the original one-level FETI method. We also report on performance comparisons on an Origin 2000 between the one- and two-level FETI methods and an optimized sparse solver, for two industrial applications: the stress analysis of a thin shell structure, and that of a three-dimensional structure modelled by solid elements. These comparisons suggest that for topologically two-dimensional problems, sparse solvers are effective when the number of processors is relatively small. They also suggest that for three-dimensional applications, scalable domain decomposition methods such as FETI deliver a superior performance on both sequential and parallel hardware configurations. Copyright


Journal of Computational Acoustics | 2006

A STUDY OF HIGHER-ORDER DISCONTINUOUS GALERKIN AND QUADRATIC LEAST-SQUARES STABILIZED FINITE ELEMENT COMPUTATIONS FOR ACOUSTICS

Isaac Harari; Radek Tezaur; Charbel Farhat

We propose an abstract two-grid algorithm with convergence independent of the coarse-space size. The abstract algorithm is applied to problems of three-dimensional linear elasticity discretized on unstructured meshes. With no regularity assumptions we prove uniform convergence with respect to coarse-space size, domain, essential boundary conditions, and jumps in Young modulus. Numerical experiments confirm the theory and show that the method works well even if some assumptions of the theory are violated.


Archive | 2003

On the Solution of Inverse Obstacle Acoustic Scattering Problems with a Limited Aperture

Rabia Djellouli; Radek Tezaur; Charbel Farhat

We present a computational methodology for retrieving the shape of an impenetrable obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well known regularized Newton algorithm, but distinguishes itself from similar optimization procedures by (a) a frequency-aware multi-stage solution strategy, (b) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (c) a numerically scalable domain decomposition method for the fast solution of three-dimensional direct acoustic scattering problems. We illustrate the salient features and highlight the performance characteristics of the proposed computational methodology with the solution on a parallel processor of various inverse mockup submarine problems.


Journal of Computational Physics | 2017

A high-order discontinuous Galerkin method for unsteady advection–diffusion problems

Raunak Borker; Charbel Farhat; Radek Tezaur

One-dimensional analyses provide novel definitions of the Galerkin/least-squares stability parameter for quadratic interpolation. A new approach to the dispersion analysis of the Lagrange multiplier approximation in discontinuous Galerkin methods is presented. A series of computations comparing the performance of Galerkin and GLS methods with Q-8-2 DGM on large-scale problems shows superior DGM results on analogous meshes, both structured and unstructured. The degradation of the GLS stabilization on unstructured meshes may be a consequence of inadequate one-dimensional analysis used to derive the stability parameter.


international symposium on neural networks | 1994

Automatic substructuring for domain decomposition using neural networks

Sugata Ghosal; Jan Mandel; Radek Tezaur

We present a computational methodology for retrieving the shape of a rigid obstacle from the knowledge of some acoustic far-field patterns. This methodology is based on the well-known regularized Newton algorithm, but distinguishes itself from similar optimization procedures by using (a) the far field pattern in a limited aperture, (b) a sensitivity-based and frequency-aware multi-stage solution strategy, (c) a computationally efficient usage of the exact sensitivities of the far-field pattern to the specified shape parameters, and (d) a numerically scalable domain decomposition method for the fast solution in a frequency band of direct acoustic scattering problems.


Journal of Computational Physics | 2016

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

David Amsallem; Radek Tezaur; Charbel Farhat

Abstract A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection–diffusion problems in the high Peclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential–algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Peclet number constant-coefficient model flow problems.

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Jan Mandel

University of Colorado Denver

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Rabia Djellouli

California State University

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Irina Kalashnikova

Sandia National Laboratories

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Antonini Macedo

University of Colorado Boulder

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Marian Brezina

University of Colorado Boulder

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Petr Vanek

University of California

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